Published on the Doomstead Diner on April 17, 2016
Discuss this article at the Science & Technology Table inside the Diner
One of the many things we have come to take for granted in the Age of Oil is the ease with which we can do long and tedious calculations, these days with electronic computers, but even before that with electronic calculators,, and before that with various types of mechanical adding machines. Nowadays, the ubiquity of machines which will do all your daily calculations has resulted in a population largely unable to just do basic arithmetic of adding, subtracting, multiplying and dividing without the aid of a calculator.
In general, if you can at least do those things, this covers you most daily math tasks a person will face in a day, unless you start building things in which case you start having to deal with angles and geometry and (gasp) even trigonometry, and then it gets worse still if you have to start multiplying up or dividing fairly large numbers, like say you have 173 Acres of land with each acre averaging 19,400 lbs/acre of organically grown carrots and you have 97 people living on your SUN☼ community property, how many pounds of carrots each year will each SUN☼ community member get?
ORGANIC CROP INFORMATION FROM:
The Owner-Built Homestead, by Ken &Barbara Kern
|#||VEGETABLE NAME||YIELD: POUNDS / ACRE|
I can tell you quite easily how many poiunds each person gets, it is 173X19400/97=34,600 lbs of carrots! That is a LOT of carrots, more than I could eat in a year anyhow. Of course, your whole 173 Acres will not be dedicated to monoculture growing of carrots, so there will be a good deal less than that amount of carrots each year coming off the property. This is just an example of a typical math problem you might face though in terms of allocating how much land to grow carrots on, how much for potatoes, how much for spinach…etc.
So how did I get that result? Well, I'm an ex-math teacher so I can ballpark this kind of calculation in my head, but I didn't do that in this case, I just Googled up a Calculator, plugged in the numbers, hit ENTER, and POOF I got the correct result! No muss, no fuss, and really fast too!
What if I did NOT have an electronic calculator at my fingertips though? Well, I could do the multiplication and long division on paper, but this is time consuming and tedious shit. Do you think Einstein did all his calculations on paper this way when he was checking out his Special Theory of Relativity? OF COURSE NOT! Einstein would still be doing the calculations today if he had tried to do it that way.
Einstein and just about every scientist or mathematician before 1970 or so who wanted to check the validity of his equations by plugging in some numbers did so by using a Slide Rule. Slide rules traditionally were manufactured in a linear format, like a regular ruler. Except you didn't use them to measure the length of lines, you used them to do quick calculations on large numbers, and to get numbers you would otherwise need to look up in a table, like logarithms and trigonometric functions.
How accurate you could be with one of these things depended on several factors:
1- How big the slide rule was. The bigger the better to spread out the scales.
2- How well machined the slide rule was. Scales had to be accurately scribed onto the rule, and the sliding part had to be very solid and not wobbly.
3- How good your eyesight and ability to estimate fractions of a space were.
Back in those days, a really high quality slide rule (usually from a German manufacturer) could cost a lot of money. For myself in HS, I just had a cheap 6" job that served its purpose pretty well. I still have it too! 🙂 As I headed off to college though, the first of the scientific calculators were being produced by Texas Instruments and Hewlett-Packard, and I coveted the HP-45, the most expensive of these coming in at $450 in 1970s dollars. I worked all summer in a shower curtain factory to afford this fabulous gizmo. With it, you could calculate everything a slide rule could, and with far more accuracy to around 12 digits as I recall. It was more expensive than the finely machined German slide rules, but actually by not that much and way more accurate and EZ to use.
These devices also got cheaper quite quickly, and by the time I graduated were about 1/2 my purchase price. Now you can get similar models for $20 of 2010 dollars. So they put the Slide Rule manufacturers out of bizness pretty quickly, except a few who produce them as novelty items and nostalgia items for aging scientists. lol.
Since they are no longer made or used much anymore, nobody learns how to use them either. Not even in science and math prep schols like Bronx High School of Science or my alma mater, Stuyvesant HS. It's one of those lost arts that probably fewer people know how to do than know how to make a stone axe out of obsidian. lol.
Recently however I began thinking about how we will do calculations for building things in a post-industrial world, stuff which we still have materials to build with and a reason for building the device. Wooden bridges to span medium size rivers, trebuchets to hurl boulders at the enemy, that sort of thing. LOL. No electronics in this projected world of the future, so we need to return to the Old Ways in this area also.
We're also not likely to have the fine machining capabilities of German factories so making really good linear slide rules would be almost as difficult as making an HP-45. Is there an answer to this problem? Yes, there is. ROUND SLIDE RULES! You can make these out of paper or cardboard or even wood or stone as long as you can cut out an accurate circle with accurately placed center, which is not that hard to do. Having Accurate scales to scribe onto your circle is necessary also, you can make these from scratch but it is tedious. Fortunately, there are numerous Circular Slide Rule templates available for FREE download online, and you can print out few to have a hard copy available when the grid goes down for good.
A serviceable slide rule is not the only thing you'll need around to to good engineering in the post collapse world of course, to make your circles to begin with you'll want to have a good Compass as well. They're not electronic so you can make one of them if need be out of a couple of sticks, but you probably won't be able to tune the size of the radius as accurately as a well machined one with a screw adjustment. For doing your designs at scale, one of these will be very handy to have in your preps.
When you are ready to scale up to your full size Trebuchet capable of hurling tons of rock at the Zombies or you want to build a Sun Dial or a Solstice calculator like Stonehenge on your SUN☼ property, you'll need to be able to measure out and draw much bigger circles. How do you do that?
Fortunately that is actually easier than the small circles for the design, all you need is some rope at the desired length of the radius and a stake driven into the ground at the center of that radius. Then walk around the circle holding the rope or string tight, and your footsteps will trace out a perfect circle. Your big circle will also prove valuable for scaling up anything, since you can use fractions of it's total radius and get a good measurement. You'll also want to have Angles marked off on both your large and small circles to do angle measurements, important for any engineering design. Marked off into 360 degrees, these circles are known to most grade school children as Protractors. A good protractor better than a cheap plastic one is another good thing to keep in your preps if you want to make accurate measurements in the post-collapse world.
However, what if you neglected to keep such a valuable tool in your bugout bag? Can you make one of reasonable accuracy with just your straight edge and compass or string & stake arrangement? Yes you can!
Dividing your circle into halves of 180 degrees is EZ, just use your straight edge to draw a straight line from the edge of the circle throuh the center to the other side. Now you have 180 degree markings on your circle.
Step 2, Bisect the line forming the diameter of your circle with your compass. I won't explain that, you should have learned how to bisect a line with a compass by the 6th grade. Draw a straight line through the bisection points, and now you are down to 90 degrees. Connect those points on the circle and you now have a perfect square. Bisect each of those lines, connect to the center, and now you are down to 45 degrees, the 8 main direction points of a Navigation compass, N, NE, E, etc.
Getting 30 degree increments is a little trickier, for this you need to take your compass set at the original radius of the circle, put the center on the edge of the circle and then draw another circle. Then you move around the circle placing the point of the compass on each place the circles intersect and draw a new circle, and then you keep moving around the original circle until you return to your start point. Assuming you did good drawing, you will get exactly 6 circles surrounding the first circle. This is called "close packing", and it's the reason Honeycombs for Bees are shaped like Hexagons, Snowflakes have 6 points and numerous other examples in the natural world.
Connect up the intersection points to each other, and you will get a perfect regular hexagon, connect to the center and you will now have 60 degree angles. You also already have 45 degree angles, so breaking up into 15 degree increments is EZ, just use your compass on the radius to measure the distance on the circle edge between the 60 and 45 degree marks and work your way around the circle marking them off as you go. You will get from this 24 increments of 15 degrees each, which is where your 24 hour clock and 12 hour analog clock face come from.
Your final divisions to get down to 360 are a bit trickier than getting down to 15 degrees. 15 is the product of two Prime Numbers, 5 & 3. So in order to get down to perfect 1 degree increments so you can be nice and accurate with your engineering projects, you have to divide this by 5 and by 3, with nothing but your compass and straight edge.
Trying to figure out how to do this is pretty tough, but fortunately a bunch of Greeks with nothing better to do with their time like Pythagoros and Archimedes worked out some methods for this a couple of thousand years ago. In the effort to not let this bit of knowledge be forgotten as we move down the collapse highway, I am disseminating it here.
To divide into 5ths, you'll need to divide your circle up into a Regular Pentagon. The interior angles of a regular pentagon are all 72 degrees. If you can do this, then 72 degrees minus 60 degrees gives you a 12 degree angle, and then a 15 degree angle minus a 12 degree angle gives you a 3 degree angle. 🙂
The problem of course here is dividing up the circle into a regular pentagon, not so EZ as a regular hexagon. Explaining how to do this in text without illustration is just about impossible, however fortunately there are Utoob tutorials on how to do it. Here is one:
The final 3 degree split to get you down to 360 one degree increments is really the toughest bear, because there is no really "pure" way to trisect an angle. When I make an impromptu protractor, I just fudge this part and eyeball it. This is good enough for most purposes, in fact for most engineering type purposes you will rarely find you need anything below 15 degrees, and 3 degrees is enough for even geodesic domes, which have pretty complex angles in them.
However, Archimedes and a few others who also had way too much time on their hands like I do did work out methods for trisecting an angle using fudges of their own. Here is the full description of how to trisect an angle from the UIUC Geometry Forum:
Most people are familiar from high school geometry with compass and straightedge constructions. For instance I remember being taught how to bisect an angle, inscribe a square into a circle among other constructions.
A few weeks ago I explained my job to a group of professors visiting the Geometry Center . I mentioned that I wrote articles on a newsgroup about geometry and that sometimes people write to me with geometry questions. For instance one person wrote asking whether it was possible to divide a line segment into any ratio, and also whether it was possible to trisect an angle. In response to the first question I explained how to find two-thirds of a line segment. I answered the second question by saying it was impossible to trisect an angle with a straightedge and a compass, and gave the person a reference to some modern algebra books as well as an article Evelyn Sander wrote about squaring the circle. One professor I told this story to replied by saying, "Bob it is possible to trisect an angle." Before I was able to respond to this shocking statement he added, "You just needed to use a MARKED straightedge and a compass." The professor was referring to Archimedes' construction for trisecting an angle with a marked straightedge and compass.
When someone mentions angle trisection I immediately think of trying to trisect an angle via a compass and straightedge. Because this is impossible I rule out any serious discussion of the manner. Maybe I'm the only one with this flaw in thinking, but I believe many mathematicians make this same serious mistake.
Why tell people it is impossible to trisect an angle via straightedge and compass? Instead we could say it is possible to trisect an angle, just not with a straightedge and a compass. When told that it is impossible to trisect an angle with a straightedge and compass people then often believe it is impossible to trisect an angle. I think this is a mistake and to rectify my previous error I will now give two methods for trisecting an angle. For both methods pictures are included that will hopefully illuminate the construction.
The first method, Archimedes' trisection of an angle using a marked straightedge has been described on the Geometry Forum before by John Conway. First take the angle to be trisected, angle ABC, and construct a line parallel to BC at point A.
Next use the compass to create a circle of radius AB centered at A.
Now comes the part where the marked straightedge is used. Mark on the straightedge the length between A and B. Take the straightedge and line it up so that one edge is fixed at the point B. Let D be the point of intersection between the line from A parallel to BC. Let E be the point on the newly named line BD that intersects with the circle. Move the marked straightedge until the line BD satisfies the condition AB = ED, that is adjust the marked straightedge until point E and point D coincide with the marks made on the straightedge.
Now that BD is found, the angle is trisected, that is 1/3*ANGLE ABC = ANGLE DBE. To see this is true let angle DBC = a. First of all since AD and BC are parallel, angle ADB = angle DBC = a. Since AE = DE, angle EAD = a, and so angle AED = Pi-2a. So angle AEB = 2a, and since AB = AE, angle ABE = 2a. Since angle ABE + angle DBC = angle ABC, and angle ABE = 2a, angle DBC = a. Thus angle ABC is trisected.
The next method does not use a marked ruler, but instead uses a curve called the Quadratrix of Hippias. This method not only allows one to trisect an angle, but enables one to partition an angle into any fraction desired by use of a special curve called the Quadratrix of Hippias. This curve can be made using a computer or graphing calculator and the idea for its construction is clever. Let A be an angle varying from 0 to Pi/2 and y=2*A/Pi. For instance when A = Pi/2, y=1, and when A=0, y=0. Plot the horizontal line y = 2*A/Pi and the angle A on the same graph. Then we will get an intersection point for each value of A from 0 to Pi/2.
This collection of intersection points is our curve, the Quadratrix of Hippias. We will now trisect the angle AOB. First find the point where the line AO intersects with the Quadratrix. The vertical coordinate of this point is our y value. Now compute y/3 (via a compass and straightedge construction if desired). Next draw a horizontal line of height y/3 on our graph, which gives us the point C. Drawing a line from C to O gives us the angle COB, an angle one third the size of angle AOB.
As I mentioned before this curve can be computed and plotted via a computer. The formula to find points on the curve is defined as x = y*cot(Pi*y/2). Yes here the vertical variable, y, is the independent variable, and the horizontal variable, x, is the dependent variable. So once the table of values is found, the coordinates will need to be flipped to correctly plot the Quadratrix.
Now a justification for the formula. In the following figure, B =(x,y) is a point on the Quadratrix of Hippias. Let BO be a line segment from the origin to B and and BOC be our angle A. If we draw in a unit circle, and drop a vertical line from the intersection of the angle we get similar triangles and see that sin(A)/cos(A) = y/x, or tan(A) = y/x. But earlier we defined a point (x,y) on the Quadratrix to satisfy y=2*A/Pi. So we get tan(Pi*y/2)=y/x or equivalently x = y*cot(Pi*y/2).
So we now have two different ways of trisecting an angle. I learned about the construction of the second method in Underwood Dudley's book: "A Budget of Trisections". In the book Dudley describes several other legitimate methods for trisecting an angle as well as compass and straightedge constructions that people have claimed trisect an angle. The book also contains entertaining excerpts of letters from these "angle trisectors".
Besides stating it is impossible to trisect an angle, I think other problems occur in discussing angle trisection. One difficulty is in explaining what it means for something to be impossible in a mathematical sense. I definitely remember in high school being told that it was impossible to trisect an angle. But I think at the time it meant the same thing to me as that it was impossible for me to drive a car. I was only 14 years old and I could not get a license to drive a car for another two years so it was just not possible AT THAT TIME. I do not remember being told that when something is impossible in mathematics, it was not possible five million years ago, it is not possible now, and it will never be possible in the future. Granted I may not have been ready for an explanation of mathematical logic and proof, but a statement like, "It is impossible to trisect an angle with a straightedge and a compass. This means it is no more possible to trisect an angle with those tools, then it is to add 1 and 2 and get 4" would have been much more powerful. (I am assuming here that we all count the same way: 1, 2, 3, 4, …)
I did not intend to attack my high school teacher; I learned an incredible amount of mathematics from her as well as a deep love for the subject. Maybe my teacher did explain what the words "mathematically impossible" meant, and I just do not remember her comments. Regardless, I think a discussion of impossible in the mathematical sense would be an interesting and valuable topic to discover in high school. Are there any teachers out there who have spent time talking about mathematical impossibilities?
I was going to detail methods for creating your own rulers for measuring distances and methods for creating your own measures of mass and weight and all the rest of the stuff we deal with in the 3D World, but I think the class is mostly asleep by now so I will stop for today for recess. Go out and PLAY!


Today I did some calculations on my motorbike. I had to convert kilometers per liter over to miles per gallon, but I figured out my gas mileage. Pretty amazing. . . We are getting 113.75 miles / gallon!! Haha. That pretty much blows the Prius out of the water. Not bad for such a little thing. Oh, I also figured out how much we’re paying for the gas. Using the current exchange rate and again converting from liters to gallons I’m paying about $1.88 per gallon at the pump. So not only is gas cheaper here, I get to go a lot farther with it at the same time. It’s a win win situation. Way to go little buddy!
https://jcjunkie.com/wp-content/uploads/2011/11/Image0073.jpg 1024 768 Josh http://jcjunkie.com/wp-content/uploads/2017/02/jcjunkielogo.png Josh2011-11-26 01:03:462017-03-14 18:42:43Little Hero. My Motorbike is AWESOME!


NN + TLD X MF + (10/NA) > 5000 = CIO
Or in words:
Where (Number of consecutive nights without unbroken sleep plus total number of times you've said 'lie down please, it's time to sleep' multiplied by minutes of fussing you've already put up with plus (10 divided by the number of adults in the house at bedtime)) all divided by Length of tether (where short = 2; medium = 5; long = 10) is greater than or equal to 5000, it's more likely than not that you will resort to crying it out to get your baby to sleep.
For me, last Wednesday, that equation looked like this:
425 + ~826 X 120 + (10/1) = 30026
In other words, I was pretty much off the charts in terms of likelihood of resorting to crying it out.
Which is what I did.
|The cry-it-out theory has its origins in a book |
published in 1894 by the guy in the middle, Dr Luther Holt.
That equation is represented as:
TBS - (MC + RT + OMGHSS + DHS) = TMS
420 - (40 + 15 + 15 + 20) = 330 (5.5 hours)
That's right folks, read it and weep. I'm rejoicing over a single stint of five and a half hours sleep. And it was still interrupted. But hey, if we follow the equation above, there's hope for even longer, uninterrupted stints.
So... I know you're wondering... Has she, overnight, become a cry-it-out convert?
The answer? Not really, no. BUT... having tried it once, and a few times since last Wednesday, I'll admit to having added 'cry-it-out' to my list of parenting theories that I may or may not put to the test... if I'm tested enough. Just consult the equation above to determine the likelihood of it being employed.


Plots the results of the JackStraw analysis for PCA significance. For each PC, plots a QQ-plot comparing the distribution of p-values for all genes across each PC, compared with a uniform distribution. Also determines a p-value for the overall significance of each PC (see Details).
JackStrawPlot( object, dims = 1:5, cols = NULL, reduction = "pca", xmax = 0.1, ymax = 0.3 )
Dims to plot
Vector of colors, each color corresponds to an individual PC. This may also be a single character
or numeric value corresponding to a palette as specified by
reduction to pull jackstraw info from
X-axis maximum on each QQ plot.
Y-axis maximum on each QQ plot.
A ggplot object
Significant PCs should show a p-value distribution (black curve) that is strongly skewed to the left compared to the null distribution (dashed line) The p-value for each PC is based on a proportion test comparing the number of genes with a p-value below a particular threshold (score.thresh), compared with the proportion of genes expected under a uniform distribution of p-values.
data("pbmc_small") JackStrawPlot(object = pbmc_small)#> Warning: Removed 83 rows containing missing values (geom_point).


Sophomore Carter Lankford offers free online tutoring service--By Mackenzie Bivin
Distance learning has been a challenge for students and teachers alike. However, for one industrious RB High student, distance learning has been the inspiration to launch a service to help his fellow students. Combining his love of mathematics and helping people, sophomore Carter Lankford is now offering free online math tutoring. Students in need can sign up on Lankford's website, coachingwithcarter.com, and Lankford will schedule an online tutoring session, using Zoom or FaceTime, to connect. According to his website, Lankford promises "[a]n experienced math tutor from the comforts of your home."
Lankford has worked with students on a variety of math levels, from 5th-grade mathematics to honors pre-calculus and AP Statistics. He also has tutored SAT math levels as he did for junior Garett Savage. Savage is a family friend of Lankford, and they discussed the idea of Coaching with Carter before Lankford offered the service. After Lankford launched the website, Savage signed up on the website for a tutoring session and has been working with Lankford ever since. According to Savage, the experience has been worthwhile.
“I’m not really good with word problems in math,” Savage said, “but [Lankford] walked me through it and put it in math terms, from English to math . . . we’ve been doing sessions over and over . . . and it’s made things a lot easier.”
According to Savage, he plans to continue to work with Lankford and would recommend it to whomever might need some extra help in math.
“I would totally recommend it,” Savage said. “He knows what he’s talking about and what he’s dealing with . . . he’s giving you one-on-one treatment of your class and the resources you need to do well.”
According to Savage, Lankford is passionate about his free online tutoring. Lankford oozed this passion when asked about why he created this service.
“During distance learning, I was trying to brainstorm ideas on how to give back to the community . . . when I saw a bunch of social media posts asking for help on problems in math,” Lankford said. “I was thinking I could probably [tutor] for most math levels . . . and I wanted to provide that outlet for [students] to get help.”
Lankford has spent the last couple of weeks providing online math help to students. Tutoring a variety of clients, Lankford has been hosting one-on-one sessions that range from thirty to sixty minutes multiple times a week. According to Lankford, he spends about four hours a week in sessions.
“I understand that kids might have trouble with multiple areas of school, whether it’s paying attention or not being able to understand the concept or a mixture of both,” Lankford said. “I make sure to provide not really a classroom setting . . . I try to build that relationship so that the participant feels more comfortable talking with me and . . . working through problems and staying calm.”
Although Lankford’s tutoring service is free, Lankford offers an option to donate. The money donated goes towards the food banks of San Diego.
“During this time, the poorer part of our community could be struggling with stores closed,” Lankford said. “They are going to need that little bit of extra help. I decided to donate all of the money I raise to food banks in order to provide for the community and help as much as possible.”
So far, Lankford has raised approximately $120. Although he hopes to continue to raise money, Lankford says that his focus is on helping people with math.
According to Lankford, he has enjoyed his experience running Coaching with Carter and plans to continue his service well after the stay-at-home order is lifted.
“I definitely want to continue this service into next school year,” Lankford said. “I plan to continue it, and I don’t plan on looking back anytime soon.”
Lankford’s service shows his dedication to his community. When a student is struggling with math, Coachingwithcarter.com provides a personalized tutoring service at no cost.


Saturday, February 11, 2012
I'm at school.
It is 9:37 in the morning and I am at school. . .I have been here since around eight for one class. Algebra. Science I can get, English I'm fine with, Music I excel at BUT math I fail at every time. As I move forward in life and get better at everything I do I still can't figure out math. I'm well aware that it is just steps. If you know the steps than you can figure it out fairly easily. I just can't seem to grasp and remember each step, it all seems very arbitrary and useless to me.


Subscribe to the Quilt Blocks Digest newsletter for updates, special offers & exclusive content!
Make a 3 patch quarter square triangle from half square triangles. Use the formula, or size chart, and see a video to make your own!
In Lesson 1 we learned to make QSTs as hourglass quilt blocks. We used two different contrasting fabrics and made two half square triangles to make our QSTs.
In Lesson 2 we learned to make Mirror Image QSTs where 2 of the 4 half QSTs are the same.
Lesson 3: 3 Patch QSTs
Here, in Lesson 3 we will learn how to make Non-Mirror Image 3 Patch QSTs (also called split QSTs). All four of the half quarter square triangles will be the same.
Triangles 1 and 2 will be small and the same size. Triangle 3 will be twice their size.
The formula for a QST is to add 1 1/4 inches to the finished size of the QST unit. Make the unit and then trim up the edges, cutting off the dog ears.
3 Patch Quarter Square Triangle Size =
Unit Finished Size + 1 1/4 inches
Adding 1 1/4 inches results in very little fabric waste. However, your stitching needs to be a very accurate 1/4 inch seam, which leaves little room for error.
Beginners may want to add 1 1/2 inches instead. Then, trim the excess fabric.
This chart includes common sizes for Three Patch QSTs. The math has been done for you!
Here's how to read the above chart:
Step 1 Cut Squares First, use the math chart above to locate the finished size of your QSTs (Column A).
From Fabric A cut 1 square and from Fabric B cut 1 square in the size noted in Column B (1 1/4 inch larger than finished size) or Column C (1 1/2 inch larger than finished size).
Next, from Fabric C cut 2 more squares the same size (Column D).
Step 1a Mark Top Square Place one Fabric A square right side up and place one Fabric B square right side down on top of it.
On the top square, place the mid-line marks of a quarter inch seam marker diagonally from corner to corner and with a pencil draw a line on both sides of the quarter inch seam marker.
Repeat for the second corner to corner.
Here are the two squares from Fabric A and Fabric B placed right sides together and 1/2 inch apart seam lines marked.
Step 2 Take the squares to the sewing machine. Orient the squares so that they will go under the needle on point (diagonally) and along the right side marked line.
Step 2a You can see the red stitching line. The blue lines indicate the stitching direction. The pencil dot indicates the top of the square, where I started stitching. You don't have to mark one on your square. It's there as a reference to make later instructions more clear.
Stitch along the right marked line until you are half way past the top intersecting line. Stop stitching. Lift up the presser foot.
Pivot the fabric counterclockwise by 90 degrees. Lower the presser foot.
Stitch the 1/2 inch distance to the next line. Stop stitching. Lift up the presser foot.
Pivot the fabric clockwise by 90 degrees. Lower the presser foot. Stitch along the left line to its end and off the fabric.
Step 2b Now, repeat Step 2a above to make the second stitching line. It should intersect with the first stitching line near the middle of the block.
Orient the squares on point (diagonally) so that the two lines that have not been sewn will go under the needle. Start stitching on the line to the right.
See the pencil dot mentioned in the previous step?... It is to the left and the lines on either side of it are now oriented horizontally.
Step 3 Using a rotary cutter and quilting ruler, cut the squares in half by cutting diagonally from one corner to corner.
Step 3a Cut the square in half again by cutting it diagonally from the other corner to corner.
Step 3b Open the quarters so the fabric is right side up. You now have four half quarter
square triangles. You've made Patches 1 and 2, the small triangles.
Step 4 Make Patch 3 Now cut the two Fabric C squares in half by placing a quilting ruler from one diagonal corner to corner and use a rotary cutter to cut them in half.
Step 4a With right sides together, pair one of the QST halves with one of the half square triangle halves. Align them along their long edges. Stitch a 1/4 inch seam.
You have now made a 3 patch quarter square triangle. (Yes, the triangle for Patch 3 is a little bigger than the half quarter square triangle because we started with 4 squares all cut the same size.)
Repeat for remaining units.
Step 5 Open the 3 patch quarter square triangles with fabrics right sides up and press the seams toward the larger triangle, or open.
What we end up with are non-mirror image QSTs. Look carefully, all the units are the same, meaning that each of the three patches of each unit is in the same place.
Having all the patches in the same place is necessary if you want all your blocks to be exactly the same.
Step 6 Square up the three patch QSTs from the center of the block where the two small triangles meet.
Divide the unfinished unit size in half (Column E in math chart above).
In this case, I'm making a 3 1/2 inch finished unit. Half of that is 1 3/4 inches.
So, on my quilting ruler I found the vertical and horizontal lines that correspond to this measurement (1 3/4 inches) and align them with the center of the block where the two small triangles meet (see where the drawn blue lines meet).
Using a rotary cutter, trim the unit along the right and top edges.
Step 7 Rotate the unit 180 degrees. Now you can align the bottom and left edges along the measurement lines that correspond to your unfinished unit size (Column F in math chart above). Here, that's 3 1/2 inches.
The center of your three patch QST should align with the measurement lines that are half of its unfinished size. (In this case, that's 1 3/4 inches.)
Be sure your unit is centered before trimming. Align the center of the unit (where the 2 small triangles meet) with the measurement lines that are half its unfinished size (here, the 1 3/4 inch measurement lines).
Use a rotary cutter to trim the unit along the right and top edges and your 3 patch quarter square triangle is squared up!
Step 8 Trim any remaining 3 Patch quarter square triangles.
Here's a video on this technique by master quilter Deb Tucker. She calls these quarter square triangles Non Mirror Image Combination Units.


During the first few weeks of term, we have been very busy in 3DS.
In maths we have been looking at addition and subtraction. We have used dienes to help us solve 3 digit addition problems and we have been working really hard to understand different types of subtraction problems and creating our own subtraction stories from a range of pictures.
During theme, we have been learning all about ourselves. We recently brought in some of our favourite toys to share with our friends. We absolutely loved this and we told each other why we liked our toys so much. We then went on to draw our favourite toy and write about it.
We have been exploring a text called “Tuesday” by David Wiesner in Guided Reading, this has really caught our attention as there are hardly any words and it is all about the antics that frogs get up to every Tuesday when they can fly! We have worked together as a whole class and in pairs discussing the different images and questioning why things are happening. The first time we saw it, we all laughed as the frogs looked so funny!
Throughout all of this learning, we have remembered how important it is to have a growth mindset and to not give up even when we find something a bit tricky!


I am not sure, but here is my best guess.
Sample Space = 2^9
(There are 9 positions, each position has two possiblities (-1 or +1) )
Favourable Outcomes :
Number of -1 in each row or coloumn should be odd.
So we get two cases here.
(i) No. of -1 in each row and coloumn is 3
(ii) No. of -1 in each row and coloumn is 1
This case can occur only when all the elements in the matrix is -1.
No. of favourable cases = 1
Consider the matrix row wise.
In the first row, you can put the -1 in any of the 3 places.
In the second row, you can put the -1 in two places (no below the previous one)
In the third row, you can put the -1 in only one place (remaining one, not below the other two).
So you get 3*2*1 = 6 possibilities in this case.
Total no. of favourable outcome = 6+1 = 7
So required probability is 7/29 ..


KU Numerical Analysis Day 2022
March 26, 2022
Department of Mathematics
University of Kansas
The KU Numerical Analysis Day provides a forum for researchers at all stages of their careers, to exchange ideas in numerical analysis, scientific computing and related application areas.
The conference will be held at the University of Kansas, Lawrence, in Snow Hall, room 120, on March 26, 2022.
Graduate students/postdocs are invited to present a poster.
The conference will provide lodging for up to two nights for invited speakers and selected graduate students/postdocs. Priority will be given to participants who have no other federal support and participants, who are students, post-doctoral scholars, or members of groups that are underrepresented in the mathematical sciences.


Foto vlăguit la 82 kg 73 kg
This page will help you to convert kilograms (kg) to pounds (lbs). If you would like to use quick kg to lbs conversion click here If you found any bug on this website contact us immediately.19.82 Kilograms to Pounds (19.82 kg to lb) Convert 19.82 Kilograms to Pounds (kg to lb) with our conversion calculator and conversion tables. To convert 19.82 kg to lb use direct conversion formula below.
pro anorexie ana pierde in greutate in greutate
The kilogram (kg) is the SI unit of mass. It is equal to the mass of the international prototype of the kilogram. This prototype is a platinum-iridium international prototype kept at the International Bureau of Weights and Measures. One kg is approximately equal to 2.2046226218487757 pounds.74 Kilograms (kg) 163.14207 Pounds (lb) Kilograms : The kilogram (or kilogramme, SI symbol: kg), also known as the kilo, is the fundamental unit of mass in the International System of Units.
calcula carbohidrați și proteine slăbire
1 kg is approximately 2.2046 pounds. To convert kilograms to pounds, multiply the number of kilograms by 2.2046. To convert kilograms to pounds, multiply the number of kilograms by 2.2046. 82 kg is approximately 180.78 pounds.Convert 85 KG to Pounds Enter amount:.


FUCK LUCK, 4-pieces set, 2 x 12,5 x 9, 3 cm and 2 x 11, 5 x 8 cm, Edition of 5+5 AP, 2016. Courtesy of the artist
The Bulgarian Sports Totalizator is the sole organization legally holding of the rights over the number games 5/35, 6/42 and 6/49. In "6 49" the participant aims to predict by one or more freely chosen by him numeric combinations, the six numbers in the numerical range from 1 to 49 which are to be drawn in the forthcoming draw, in which the participant will participate. The amount of the prize in each winning group depend son the number of combinations that have correctly predicted the winning combination. The six numbers i drawn in each block composes the title you can read from left to right.
Installation view: IN THE LABELLING GAP ehxibition, 05 April 2016 - 08 May 2016, Sofia City Art Gallery


12 Calculators You Need
Making maths problems a thing of the past, this app puts a dozen calculators for loans, tips, mortgages and a whole lot more in your pocket.
12 Calculators You Need Review
by on March 13, 2010
Mobile phones have unfortunately made the humble pocket calculator obsolete. But your phone won’t help you when you need to do difficult things like work out percentages or stop the fights when the price of a meal needs to be split four ways.
That’s where 12 Calculators You Need comes in. Instead of racking your memory for anything you remember from your Maths lessons, this money app does exactly what it says on the tin, with a dozen number crunching options to guide you safely through the mathematical maze.
The calculators the app offers include ones for mortgages, loans, health, currency conversion and even tips. Each one has an easy to use interface and will turn you into a maths whizz, without making you socially inept or the subject of bullying.
Instead of hitting you with complicated equations, each calculator uses a slider to help you with your mathematical problems.
We’re not too sure why there are 12 calculators on show here – Tips and Simple Tips could be combined, as could Auto Loan and Loan calculator – and even though it costs $1 to buy, it will save you in the long run.
RBS Six Nations Live Challenge
Take on your mates in a Six Nations (quiz) clash for the ages and win match balls from the competition...
The best of the Beeby Sound
Are we really that obsessed with virtual Polaroids?
Limited ability to save online videos
It’s Wikipedia in an easy to use format
Nothing to be seen here
Tom And Jerry
It’s all the Tom and Jerry cartoons, and it’s brilliant
Loads of effects but get ready to wait
Thumba Photo Editor
A worthwhile investment into photo editing
A clock you’ll never need


I regularly build and interpret a wide range of statistical models. I can help you build and understand linear models (e.g. ANOVA, regression) and generalised linear models (e.g. analyses of Poisson and binomial data). I can also help you with mixed models if you are keen to understand random effects. I have quite a few years of experience with R and can guide you to solve your coding/programming questions.
For my PhD research, that investigates the evolution of cooperation and its environmental drivers, I am working with genomic data and can also provide help if your project involves bioinformatics (e.g. UNIX) or the analysis of genetic variation (e.g. SNPs, microsats).


ARE 210 (PhD Probability and Statistics) Fall 2022
- Sigma Algebras and Independce
- Conditional Expectations and Conditional Sigma Algebras
- Probability and Distribution Limits
- MLE and the Invariance Property
ARE 210 (PhD Probability and Statistics) Fall 2021
- Conditional Expectations and Characteristic Functions
- Distributions of Multivariate Transformations and Convergence of Combinations of Sample Statistics
- Exponential Families, Identification, and MLE
- MLE with a closed parameter space, GMM, and the finite sample distribution of MLE.
- Asymptotic distribution of estimators and hypothesis testing.
- Efficient GMM, Proving Statistics are Complete, UMVUEs, and the Cramer-Rao Lower Bound


following colorful and fun number flashcards
have been created to encourage children to learn
Spanish numbers from an early age. These numbers in
words flashcards include Spanish flashcards with
pictures for number zero, one, two, three, four,
five, six, seven, eight, nine and number ten with
numerals and number words in Spanish and English
languages. The characterized number pictures
make learning Spanish with flashcards interesting to capture the
attention and imagination of children. This is a
very useful, free teaching resource which may be
used by schools, teachers and tutors of the
Spanish language. The number flashcards with
pictures are free to everyone and very simple to
print. Please follow the printing instructions
at the bottom of this page for information about
how to print number flashcards.
Kids can learn the numbers in Spanish and English from
very young. Showing number flashcards to babies will
encourage their speech and pronunciation when they start
speaking Spanish. This is a very fun way to learn
Spanish, particularly for younger kids such as
preschoolers, kindergarten, infants, toddlers and first
grade children. There are audit videos on many pages of
this website to help children with their pronunciation
of Spanish words and vocabulary including the numbers in
Spanish and how to say them correctly. The audio videos
can be paused at any point to allow kids time to
practice listening to the sound of the numbers and
saying the numbers aloud. This is a great way for
children to gain confidence with speaking Spanish and to
check that their pronunciation is correct.
Print Number Flashcards:
The Spanish number flashcards are printable for free to
everybody. Each card can be printed in small or large
sizes very easily. To print a study card right click on
the image and select print. The number cards with
pictures on this page will print out small cards. To
print a big flashcard, simply select the link below the
relevant image which will open up a larger version of
the selected number image. Spanish teachers may print
this set of number flashcards for free as they make
excellent handouts for school kids to take home to use
as a study aid for practicing the numbers in Spanish.
The bright, high quality flashcard number pictures will
help children to remember the numbers and associate the
numerals with the English and Spanish words for numbers.
Flash cards can be used to create a fun activity or
learning game for kids practicing the different numbers
in Spanish or English number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and
number 10 flashcards.
Numbers Pronunciation Video - How to count from 1 to 10
Printable Spanish Number Flashcards for Kids and ideas for lesson planning and teaching languages.
Fun study cards for Toddlers and Kids free and easy to print. Basic study cards, study games and activities for children.
Free printable number flash cards for kids and teachers.
Spanish picture cards with numbers 1-10 cero, uno, dos, tres, cuatro, cinco, seis, siete, ocho, nueve y diez
All images are hand drawn and copyright belongs to Sarah Johnstone


Like my officemate Mel , I was able to get advance access to Pottermore ! The question that we answered is: In the Gryffindor versus Slytherin Quidditch match, in Harry's third year, how many points is Gryffindor leading by before Harry catches the Golden Snitch? Multiply this number by 35. The answer is 2100. You need to levitate the magic quill before it will allow you to register. And here is my welcome screen: Yey! Note: For those who would like to register for the succeeding days, I think new day arrives here in the Philippines at around 6pm.


Continuation from Last Week
This week we were able to launch our catapults and complete our project from last week. Not once, not twice but four times! Let me introduce you to the catapults.
From Table 1, with a high flying fling, please welcome The Catapult!
From Table 2, with a simple but powerful shot, please welcome The Catapult!
And last but not least from Table 3, with the furthest-going projectile, please welcome The Catapult!
These three catapults competed against each other in the initial launch. The next day their catapulting abilities were put to the test as everyone discovered what happens when the mass of an object increases and the motion that this growing mass creates. Conclusion: The greater the mass, the shorter distance it will travel with the same amount of force. This also means, the greater the mass, the greater the force needed to move it.
Before we did anything with fractions, I asked the students three questions. What are fractions? Which cookie would you rather have a half? (giving them the choice between two cookies of varying sizes). Where can we use fractions in daily life?
After some silent contemplation, we discussed. We decided that a fraction was ” a whole divided into equal parts.” Everyone naturally wanted the larger cookie half which led us to talking about different wholes equal a different sized fraction. Then we started talking about why on earth we study fractions at all. What’s the point? When will we ever use fractions again? The students came up with dividing sections within a group (especially in sports), sharing, baking, and shopping (especially with coupons). Then I pointed out to them photography is all about fractions. As you have probably already realized and as I have mentioned earlier, I love to use photography to tell a visual story. I have noticed that bringing in my excitement for something in the classroom makes the students excited.
We talked about shutter speed that is written as a fraction of a second. It is the amount of time that the shutter stays open. A faster shutter speed with a larger denominator (ex 1/1000) can freeze motion like water drops or a speeding car. A slower shutter speed with a smaller denominator (ex 1/20) would blur motion creating a misty water or a blur of motion as a car zooms by the photographer.
Then we talked about aperture, or how wide the shutter is. The wider the opening, the smaller the number. The smaller the opening, the larger the number. I confessed to the children that this confused me initially until my brother told me to look at it like a fraction. 1/5 is bigger than 1/22 so f/5 is larger than f/22
With that, I allowed the children to practice their new photography skills by taking pictures on my two cameras. Below is their work as they tested out different settings and discovered more about fractions.
The next day we created fraction strips to help us to understand what a fraction is. We also used these to understand and discover equivalent fractions. After only just a few days with fractions, fractions don’t seem as scary anymore.


Recently, I came across a stat that was surprising to fathom in the tennis world. Any tennis lover would agree that the three greatest tennis players over the last 3 years to play together would be Roger Federer, Rafael Nadal and Novak Djokovic. It was interesting to note that the 3 players who dominated tennis amongst themselves over the last 15 years have the below stats:
A win percentage of total career points played:
The interesting point about this stat is the narrow range of the total number of points the best 3 have won over a 15-year career. This is not something that the human brain would intuitively think about. In order to understand this better, I had to take help from the above game which breaks down scenarios in a more intuitive way:
The site above simulates a tennis match, where the user can assign a probability of a player winning a point. So, assume you give Player A, a 55% probability of winning a point, the site calculates the probability that Player A wins a 5 set match. If one plays around with this, you understand that the probability of Player A winning a 5-set match (with a 55% probability of winning a point) becomes 95% (what we in English would define as a near-certain event).
The numbers stack up very similar to probabilities in investing. A study of investment legends who have managed money over 30 years, shows that their individual track record of a positive return (of each decision – being a stock) would be around 55-60%. When this is combined with the benefit of time and prudent risk management, they outperform significantly over the market.


Homework Questions for Chapter 16 - Climate Change
SHOW ALL WORK , CIRCLE THE CORRECT ANSWER, PLEASE BE NEAT AND STAPLE YOUR HOMEWORK!
ALSO, PLEASE USE A SPREADSHEET FOR ALL GRAPHS
Follow the Problem solving steps discussed in class
1. Since the earth's temperature has remained essentially constant with time, it can be assumed that the incoming solar radiation absorbed by the earth is equal to the IR radiation emitted by the earth. Therefore, radiation in (SW) = radiation out (LW). This is called radiative equilibrium.
a. If you were looking at the earth from outer space, what geometrical cross section area would the earth appear to have? Your answer should be a formula for area.
b. Now, how many watts of solar radiation will the earth absorb at any given time. Express your answer in terms of the the solar constant (S) given in watts per square meter. Assume that the earth is absorbing 100% of the total incident radiation.
c. We know the earth does not absorb all incident radiation. Given that the planetary albedo is A, how many watts of incoming solar radiation is the earth absorbing?
d. Over what geometrical area is the earth reemitting back LW radiation to space?
e. How many total watts of radiation are being emitted back to space at any given time? Your answer to this question should include Te, the radiative equilibrium temperature of the earth.
f. Assuming that the earth is in radiative equilibrium, use the results above to calculate the radiative equilibrium temperature, Te.
g. Is the result in (f) physically reasonable? Explain


The Cone Over a Projective Variety. Let be a nonempty algebraic set, and let be the map which sends the point with affine coordinates to the point with homogeneous coordinates . We define the affine cone over to be
- Show that is an algebraic set in , whose ideal is equal to , considered as an ordinary ideal in .
- is irreducible if and only if is.
Sometimes we consider the projective closure of in . This is called the projective cone over .
Proof of a. since consists of all scalar multiples of points in , i.e., all points in that are zeros of the generators of .
Proof of b. is irreducible if and only is prime if and only if is prime (by a) if and only if is irreducible.
Proof of c. by Problem 2.6.


Meet the wonderful world of geometry with the octagon puzzle from New Classic Toys. Create a whole range of different shapes and figures with the 72 triangular wooden blocks in the frame. This octagon puzzle offers endless puzzle possibilities, both inside and outside the frame. Let your imagination run free! This beautiful puzzle is ideal for the development of creativity, problem-solving ability and pattern recall. In addition, playing with this set stimulates the development of fine motor skills. For hours of fun! From 3 years.


5 Senses Coloring Pages Inspirational Math Worksheets Draw 5th Grade About Remodel Download Of 5Th
Tremendous 5th Grade Coloring Pages Of 6th 1024×768 Ruva 5Th 5Th Grade Coloring Pages Math Coloring Worksheets 1st Grade 5th Printable Science Color By 810×1024 5Th Pages Coloring Pages 5th Grade Fresh Fun For 3rd Graders Halloween Of 5Th 5th Grade Coloring Pages For Children Insider Graders Mssrainbows 1024×791 5Th Free Math Coloring Worksheets 5th Grade Thanksgiving Activities Color By Number Sheets Multiplication Two 791×1024 5Th Pages Tremendous 5th Grade Coloring Pages Beautiful Unique Math Free Worksheets For 6th Inspirational Gam Fun Worksheet Sixth Puzzle Pdf Review Printable Book 1024×1325 5Th Phenomenal Free Printable Winter Coloring Pages Picture Ideas Book World 5th Grade Preschool Activities Worksheets Astonishing 5Th 4th Grade Coloring Pages Beautiful Math Sheets Of 5Th 5th Grade Coloring Pages 21 5Th 5Th Grade Coloring Pages Inspiration Coloring Third Grade Pages At Getdrawings Com Free For Personal 3rd Tremendous Picture 5Th 5th Grade Coloring Pages New For 4 4336 816c2971056 Of 5Th Coloring Pages 5th Grade Christmas Barbie Free Kitten 5Th .
5th Grade Coloring Pages New For 4 4336 816c2971056 Of 5Th
Inspiration Coloring Third Grade Pages At Getdrawings Com Free For Personal 3rd Tremendous Picture 5Th
On this website we recommend many designs about 5Th Grade Coloring Pages that we have collected from various sites. chicagolawyers that we have collected from various sites, and of course what we recommend is the most excellent of image for 5Th Grade Coloring Pages. If you like the design on our website, please do not hesitate to visit again and get inspiration from all the houses in the design of our web design.


‘Although fractals are very complex shapes,
they are formed by repeating a simple process over and over’
Jonathan Wolf www.fractalfoundation.org
I want to pursue the thought that the shamanic world view is essentially as pragmatic as any scientific pursuit here. Both are based on astute observation of the world around us. They use very different language to describe their interactions. It is in the places where the filter of language intersects that we might be able to get a glimpse of what is common to both. This card deck representing a contemporary World Tree is essentially a fractal map. What does that mean?
A French mathematician named Mandelbrot coined the term fractal in 1975 to describe a specific kind of mathematical concept that addressed repeating patterns in nature as well as in theory. Computers have allowed people to see the fractal patterns these kind of equations create even though mathematicians are still arguing about how to define them. The criteria the mathematicians have agreed on are remarkably similar to the qualities of the shamanic World Tree.
Mathematicians say that fractals are self-similar, echoing an ancient alchemical concept of the microcosm as a complete mirror of the macrocosm. They transcend scale, and their patterns are interconnected. They are not limited to geometrical shapes in the material world, but can describe processes occurring in time. Like shamans, fractals tell the story of the process that creates them. Most wondrously, with fractals as in nature, universal rules result in infinite diversity and beauty.
The language of numbers appears to have had limited appeal in human culture, while metaphors of images, journeys, and relationships endure. While the mathematician will talk about the inherent lines of symmetry in a fractal image, the shaman will describe the trunk of the world tree.


The ever eccentric creator of Mortal Kombat; Ed Boon has taken to twitter in what some call a case of massive trolling in which that would rival Yoshinori Ono’s tweets. I think it’s cool that he wants to educate us today.
Ed Boon’s mysterious tweets all involve mathematical questions. Basic 4th-5th grade stuff that we did as kids:
Square root of 841.
— Ed Boon (@noobde) May 4, 2014
The answer is 29
Question: How many days in (non-leap-year) February?
— Ed Boon (@noobde) May 5, 2014
I’ll save you the time. The answer is 28. It could mean a countdown. 28 days til Netherrealm announces MK 10 or Injustice 2? I kind of though of this:
28, 2+8 = 10= Mortal Kombat 10!
Another math tweet counting down to 27:
Man, I love the Simpsons.https://t.co/8venKdql5n
— Ed Boon (@noobde) May 6, 2014
The video is a funny reference from a Simpsons in which the plot revolved around Lisa conquering math. So now it’s 29, 28, 27. The next tweet is obviously 26 related. Mortal Kombat 10 is likely.by


3 edition of Game Theory and Applications (Game Theory & Applications) found in the catalog.
by Nova Science Publishers
Written in English
|Contributions||L. A. Petrosjan (Editor), V. V. Mazalov (Editor)|
|The Physical Object|
|Number of Pages||202|
This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence.5/5(1). "Game Theory is a most active and constantly expanding field. Young and Zamir, top game theorists, have selected world-leading specialists to provide excellent surveys of most relevant topics in recent theoretical research in game theory and its applications." --Sergiu Hart, .
Game Theory and Its Applications book. Read reviews from world’s largest community for readers. Andrew Coleman provides an accessible introduction to the /5(1). A 'game' is any social situation involving two or more players in which the interests of both are interdependent. Underlying the structure of game theory is an assumption of 'rationality', i.e. that players act to produce the best possible outcome for themselves. These concepts now pervade much of social science, but many people remain unconvinced or lack the skills to adapt the models to.
Game Theory and the Law; Harvard University Press, ; Management & Business: Edited by Kalyan Chatterjee and William F. Samuelson Game Theory and Business Applications; Kluwer Academic Publishers, ; Avinash K. Dixit and Barry Nalebuff The Art of Strategy: A Game Theorist’s Guide to Success in Business & Life; WW Norton & Company, Mathematical Game Theory combines both the theoretical and mathematical foundations of game theory with a series of complex applications along with topics presented in a logical progression to achieve a unified presentation of research results. This book covers topics such as two-person games in strategic form, zero-sum games, N-person non Brand: Wiley.
Harvesting native hay in the Mouse river valley of North Dakota
Structural characteristics of the Ontario-Quebec urban system [by] T. Bunting and A.M. Baker.
Essentials of pediatric nursing.
constitutions of the Australian states
U.S. WOCE implementation plan
Need-based Educational Aid Antitrust Protection Act of 1997
Social science generalizations for use in the social studies curriculum
High resolution numerical modelling of the atmosphere and ocean
Young ladys guide.
Data structures for engineering software
Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule.
The papers and abstracts collected here explore its recent development and suggest new research. Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to game theory.
It opens with the theory of two-person zero-sum games, two-person non-zero sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory by: Introducing Game Theory and its Applications (Discrete Mathematics and Its Applications Book 21) - Kindle edition by Mendelson, Elliott.
Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Introducing Game Theory and its Applications (Discrete Mathematics and Its Applications Book /5(3).
This is a business book explaining many applications of game theory. The discussions of “changing the game” and “added values” are crucial for anyone in business. Game Theory: An Introduction by Steve Tadelis. This is a textbook on game theory suitable for. Game Theory with Applications to Economics (2nd edt) Friedman, J.
Published by Oxford University Press Inc () ISBN Good. This is an ex-library book and may have the usual library/used-book markings book has hardback covers. In good all round condition. Please note the Image in this listing is a stock photo and may not. What are the applications of game theory for real life.
That’s a central question: Is game theory useful in a concrete sense or not. Game theory is an area of economics that has enjoyed fantastic public relations.
John Von Neumann, one of the founders of game theory, was not only a genius in mathematics, he was also a genius in public relations. This book provides a wide range of examples of the uses of game theory, even in situations where such application may seem unsuitable.
This book explores cooperative, competitive, leader-follower games and the free-rider problem - as well as games with the aim of maintaining friendships or team work.
The reader will be presented with a wide range of practical applications of game theory. Game theory is the study of mathematical models of strategic interaction among rational decision-makers.
It has applications in all fields of social science, as well as in logic, systems science and computer ally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. framework of game theory. Students and faculty alike will ﬁnd this concise, rigorous and clear introduction to the main ideas in game theory immensely valuable.” —Marcus Feldman, Stanford University, Biology “This unique book is today the best short technical introduction to game theory.
In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more.
The book (A Beautiful Mind, by Game theory is a standard tool of analysis for professionals working in the fields of operations research. Game Theory Through Examples, Erich Prisner Geometry From Africa: MathematicalandEducational Explorations,Paulus Gerdes Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor Katz and Karen.
Games of Strategy: Theory and Applications, originally published by Prentice Hall inwas written by Melvin Dresher, a RAND research mathematician, during the heyday of Game Theory at book introduced readers to the basic concepts of game theory and its applications for military, economic, and political problems, as well as its usefulness in decisionmaking in business, operations.
Download Game Theory And Its Applications In The Social And Biological Sciences books, Andrew Coleman provides an accessible introduction to the fundamentals of mathematical gaming and other major applications in social psychology, decision theory, economics, politics, evolutionary biology, philosophy, operational research and sociology.
The purpose of Game Theory and Business Applications is to show how game theory can be used to model and analyze business decisions.
The contents of this revised edition contain a wide variety of business functions – from accounting to operations, from marketing to strategy to organizational design.
The first tutorial style book that gives all the relevant theory, at the right level of rigour, for the wireless communications engineer; Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real world resource allocation problems.
Dynamic Games and Applications is devoted to the development of all classes of dynamic games, namely, differential games, discrete-time dynamic games, evolutionary games, repeated and stochastic games, and their applications in all fields, including: * biology * computer science * ecology * economics * engineering * management science * operations research * political science *.
game theory are forced to rely on textbooks written by and for econo-mists. While there are many excellent economic game theory texts, their treatments of the subject are often not well-suited to the needs of many political scientists. First and perhaps most importantly, the applications and topics are generally those of interest to economists.
I am no math whiz but was curious about Game Theory as well. If you are looking for something totally general and have heard of Game Theory but don't entirely grasp even what it even is, I would watch the scene in "A Beautiful Mind" where Nash d. In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.
If each player has chosen a strategy—an action plan choosing. This volume constitutes the refereed post-conference proceedings of the 3rd Joint China-Dutch Workshop on Game Theory and Applications and the 7th China Meeting on Game Theory and Applications, GTAheld in Fuzhou, China, in November Recent years have witnessed a lot of applications in the computer science, especially in the area of the wireless networks.
The applications can be divided into the following two main categories: applications in the network performance and those in the energy efficiency. The game theory is widely used to regulate the behavior of the users; therefore, the cooperation among the .Chatterjee and Samuelson: Applications of Game Theory 2 This first generation of game theoretic models revolutionized finance but much remains to be explained.
Game theoretic methods continue to develop and we believe that extensions involving richer informational models are especially relevant for finance. In Section 3, we review recent work.


100 Fun and Easy Learning Games for Kids: Teach Reading, Writing, Math and More with Fun Activities by Amanda Boyarshinov and Kim Vij
We are unable to find iTunes on your computer. To download the free app Monster Math 2: Fun Free Learning Games for Kids by Makkajai Edu Tech Private Limited, get iTunes now.
The first online platform reviewed in this article is Learning Games For Kids. The website serves to be a right place for elementary and preschool kids who can learn various skills required to be learnt at their level. The website not only includes games, but also online lessons, songs, rhymes, etc. that help children in their overall development. It focuses on building language skills, improving ability to solve math problems, teaching science facts through songs, social science lessons, and much more. These lessons, songs, and games are divided into different categories like math facts, math games, science songs, animal and nature games, word games, art and music games, and much more. All these games are available free of cost and you can enjoy them without creating any account or anything. Check out the link above.


what is the rule of 72?
The rule of 72 is a calculation that estimates the number of years it takes to double your money at a specific rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. in this case, 18 years.
The same calculation can also be useful for inflation, but it will reflect the number of years until the initial value has been halved, rather than doubled.
The rule of 72 is derived from a more complex calculation and is an approximation, so it is not perfectly accurate. the most accurate rule of 72 results are based on the 8 percent interest rate, and the farther you go from 8 percent in either direction, the less accurate the results will be. Still, this handy formula can help you better understand how much your money can grow, assuming a specific rate of return.
the rule of 72 formula
The rule of 72 can be expressed simply as:
years to double = 72 / rate of return on investment (or interest rate)
There are some important caveats to understand with this formula:
- The interest rate should not be expressed as a decimal of 1, such as 0.07 for 7 percent. it should just be the number 7. So, for example, 72/7 is 10.3 or 10.3 years.
- The rule of 72 focuses on compound interest compounded annually.
- for simple interest, simply divide 1 by the interest rate expressed as a decimal. If you had $100 at a 10 percent simple interest rate with no compounding, you would divide 1 by 0.1, which would give you a 10-year doubling rate.
- for continuous compound interest, you will get more accurate results if you use 69.3 instead of 72. the rule of 72 is an estimate, and 69.3 is more difficult for mental math than 72, which is easily divided by 2, 3, 4, 6, 8, 9, and 12. However, if you have a calculator, use 69.3 to get slightly more precise results.
- The further away you are from an 8 percent return, the less accurate your results will be. the rule of 72 works best in the 5 to 12 percent range, but it’s still an approximation.
- To calculate based on a lower interest rate, such as 2 percent, reduce 72 to 71; to calculate based on a higher interest rate, add one to 72 for every three percentage point increase. so, for example, use 74 if you’re calculating the doubling time for 18 percent interest.
how the rule of 72 works
The actual mathematical formula is complex and derives the number of years until it doubles based on the time value of money.
I would start with calculating the future value for periodic compounding rates of return, a calculation that helps anyone interested in calculating exponential growth or decay:
fv = pv*(1+r)t
fv is the future value, pv is the present value, r is the rate, and t is the time period. to isolate t when it is in an exponent, you can take the natural logarithms of both sides. Natural logarithms are a mathematical way of solving for an exponent. a natural logarithm of a number is the logarithm of the number raised to e, an irrational mathematical constant that is approximately 2.718. Using the example of a doubling of $10, deriving the rule of 72 would look like this:
20 = 10*(1+r)t
20/10 = 10*(1+r)t/10
2 = (1+r)t
ln(2) = ln((1+r)t)
ln(2) = r*t
The natural log of 2 is 0.693147, so when you solve for t using those natural logs, you get t = 0.693147/r.
Actual results are not round numbers and are closer to 69.3, but 72 breaks down easily for many of the common rates of return people earn on their investments, which is why 72 has gained popularity as a value for estimate the doubling time.
For more accurate data on how your investments are likely to grow, use a compound interest calculator based on the full formula.
how to use the rule of 72 for investment planning
Most families intend to continue investing over time, often monthly. You can project how long it will take to reach a given target amount if you have an average rate of return and a current balance. If, for example, you have $100,000 invested today at 10 percent interest and you are 22 years from retirement, you can expect your money to double about three times, going from $100,000 to $200,000, then to $400,000, and then to $800,000.
If your interest rate changes or you need more money due to inflation or other factors, use the results of the rule of 72 to help you decide how to keep investing over time.
You can also use the rule of 72 to choose between risk and reward. If, for example, you have a low-risk investment that pays 2 percent interest, you can compare the doubling rate over 36 years with that of a high-risk investment that pays 10 percent and doubles in seven years.
Many young adults just starting out choose high-risk investments because they have the opportunity to take advantage of high rates of return for multiple doubling cycles. Those approaching retirement, however, will likely choose to invest in lower-risk accounts as they get closer to their retirement target amount because doubling down is less important than investing in safer investments.
rule of 72 during inflation
investors can use the rule of 72 to see how many years it will take for their purchasing power to be halved due to inflation. For example, if inflation is running around 8 percent (as in mid-2022), you can divide 72 by the inflation rate to get 9 years until the purchasing power of your money drops by 50 percent.
72/8 = 9 years to lose half of your purchasing power.
The rule of 72 allows investors to realize the seriousness of inflation in a concrete way. Inflation may not stay elevated for such a long period of time, but it has in the past over a period of several years, which really hurt the purchasing power of accumulated assets.
The rule of 72 is an important guideline to keep in mind when considering how much to invest. Investing even a small amount can have a big impact if you start early, and the effect can only increase the more you invest, as the power of compounding works its magic. You can also use the rule of 72 to assess how quickly you can lose purchasing power during periods of inflation.
note: georgina tzanetos from bankrate contributed to a recent update to this story.


Torrence Douglas Parsons (1941–1987) was an American mathematician.
He worked mainly in graph theory, and is known for introducing a graph-theoretic view of pursuit-evasion problems (Parsons 1976, 1978). He obtained his Ph.D. from Princeton University in 1966 under the supervision of Albert W. Tucker.
- Parsons, T. D. (1976). "Pursuit-evasion in a graph". Theory and Applications of Graphs. Springer-Verlag. pp. 426–441.
- Parsons, T.D. (1978). "The search number of a connected graph". Proc. 10th Southeastern Conf. Combinatorics, Graph Theory, and Computing. pp. 549–554.
Memorial articles in
- Journal of Graph Theory vol. 12
- Discrete Mathematics vol. 78
|This article about an American mathematician is a stub. You can help Wikipedia by expanding it.|


Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format. Create the worksheets properties of inequalities pdf need with Infinite Algebra 1.
Adding and Subtracting Rational Numbers. Multiplying and Dividing Rational Numbers. Trigonometry to Find Angle Measures. Systems of Equations Word Problems. Adding and Subtracting Rational Expressions.
Center and Spread of Data. Distance Rate Time Word Problems. Adding and Subtracting Radical Expressions. Teaching Math Just got a Whole Lot Easier. Graphical and substitution methods for solving systems are reviewed before the development of the Elimination Method. Modeling with systems of equations and inequalities is stressed.
Finally, we develop the idea of using graphs to help solve equations. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. We are a small, independent publisher founded by a math teacher and his wife.
We believe in the value we bring to teachers and schools, and we want to keep doing it. We keep our prices low so all teachers and schools can benefit from our products and services. We know it’s nice to share, but please don’t share your subscriber content or your login or validation info. Answer Keys, editable lesson files, pdfs, etc.


USDMXN Bulls Lie In Wait Orbex Forex Trading Blog Lie, Forex trading, Bull
• For instance, a stock goes from 50 to 100, and then back to 75. In order to find the Fibonacci extension levels, you have to find the recent significant Swing High and Swing Low. • It can be used to find projected areas of support or resistance when the price is moving into an area where other methods of finding support or resistance are not Pacific Financial Derivatives Background and Safety applicable or evident. • Extension levels are also possible areas of interest where the price may stall or reverse. Do not trade in “Options” based on recommendations from unauthorised / unregistered investment advisors and influencers. Understand the basics of swing trading and how it uses volatility within the market to its advantage.
Similarly, values can be calculated for the other ratios as well. This is everything you need to know about Fibonacci retracement and extension levels. Keep reading and revising until you learn everything written in this post. • Fibonacci retracements provide levels for a pullback whereas Fibonacci extensions provide levels to move in the direction of the existing trend. • Fibonacci extension levels indicate a price area that will be significant for the stock after the pullback/correction is over.
23.6%, 38.2%, 50%, and 61.8% are the important Fibonacci retracement levels. According to the identified results, they help traders identify the probable extent of the retracement and position themselves for the trade. After selecting the Fibonacci retracement tool from the charts tool, the trader must click on the trough first and drag the line to the peak.
One is that using Fib levels alone could result in a lower trading accuracy, especially in a choppy environment. As a result, traders need additional trading tools to back up all the signals generated by retracement or extension levels plotted on the chart. Fibonacci retracement lines reflect crucial areas where a stock may reverse or stall in technical analysis. The standard ratios comprise 23.6%, 38.2%, and 50%, apart from others. They will come between a high point and a low point for a stock.
Exhibit: Fibonacci retracement in a downtrend
You need to apply the parallel projection or growth projection principle which you can find on my book onFibonacci Method. The study of fibonacci method will not get complete without studying the clusture, and phi ellipse. Same way the fibonacci fan line also the finest tool one can use for short term trend analysis. You can get many more successful examples on fibonacci method success in real trade practice under the section my experiment on fibonacci method.
The levels of 23.6 per cent, 38.2 per cent, 50 per cent, 61.8 per cent, and 78.6 per cent are the major retracement levels to consider while analysing a stock. If the price rises to Rs.1000, and then drops to Rs.236, it has retraced 23.6%, which is a Fibonacci number. Fibonacci numbers are found all over the nature, and therefore many traders are of the belief that these numbers have significant relevance in the financial markets. While Fibonacci retracements apply percentages to a pullback, Fibonacci extensions apply percentages to a move back in the trending direction.
The prior trend of this 4700 high was a rising trend started from 4000 then it is classified as growth retracement. Now the next big question is how do I will know that 4350 support is a valid support or is a mathematical eye wash for me. By simple observation if I will find the fall below 4350 invites buying and escalates the price to bit higher level then I will conclude this price is a valid support. If the price action is rising in nature but in between some correction brings down the price and again escalate to higher levels then we can this Retracement as a growth Retracement.
Things changed in late February when markets realised that Covid-19’s impact on insurers could be significant. Insurers are yet to know the full impact of the crisis as governments and regulators nudge them to give moratoriums to policyholders and quickly settle claims too. India’s insurance regulator has set strict deadlines for medical insurers to settle Covid-19 claims. General insurers face damage claims from businesses devastated by the national lockdown to contain the disease. If the price action is in falling in nature but in between some technical bounce back.
Trading with Fibonacci levels – Learn how to use this basic technical analysis method
Combining it with other technical indicators would help reduce the scope of inaccuracies and, thus, enable the traders to make better trading decisions. The significant Fibonacci ratios are the retracements of 23.6%, 38.2%, 50%, and 61.8%. These ratios aid traders in determining the likely extent of the retracement and in choosing the appropriate trading position. When you anticipate a correction following a sudden upward or downward movement, you might use Fibonacci analysis in the stock market.
What is the best way to use Fibonacci retracement?
In a downtrend:
Step 1 – Identify the direction of the market: downtrend. Step 2 – Attach the Fibonacci retracement tool on the top and drag it to the right, all the way to the bottom. Step 3 – Monitor the three potential resistance levels: 0.236, 0.382 and 0.618.
However, the way to get them is to start with the Fibonacci numbers. This article will go through what the Fibonacci retracement tool is and how you can use it to find important levels on a chart. Below is the Amibroker AFL to plot Fibonacci levels from 0 to 100%, this AFL can be used to develop any strategy on Fibonacci retracement. The equity market, or what people commonly refer to as the stock market, has a number of segments a…
Fibonacci retracement is created by taking two points a major peak and a trough. Then the vertical distances are divided into key Fibonacci ratios fibonacci method trading i.e. 23.6%, 38.2%, 50%, 61.8%, 78.6% and 100%. After the levels are defined, horizontal lines are drawn to identify support and resistance levels.
Unlike moving averages, Fibonacci retracement levels are static prices that do not change. The static quality of the price levels enables quick and easy identification. Fibonacci retracements can be used in order to place entry orders, to calculate stop loss, or to set price targets. Let’s learn with an example, a trader sees a stock moving higher.
- The stock retraced back 38.2% to Rs.319 before continuing its up-move.
- In order to find the retracement levels, you have to find the recent significant Swing High and Swing Low.
- To understand this better consider a trader who examines a stock to have moved higher only for it to retrace to the 38.2 % level.
- In an uptrend, one needs to attach the Fibonacci retracement tool on the bottom and drag it to the right, all the way to the top.
They simply refer to the percentages of the price range under consideration. An easy way to learn everything about stocks, investments, and trading. Though the retracement levels demonstrate where the price might find support or resistance, there are no guarantees the price will stop there. For this reason, other confirmation signals are often used, such as the price beginning to bounce off the level.
Fibonacci Retracements: The Complete Overview
When the market is trending upward, traders go long on a retracement at a Fibonacci support level. Additionally, when the market is trending downwards, traders go short on a retracement at a Fibonacci resistance level. Technical analysis also employs Fibonacci levels as is evident from the Elliot Wave theory and Gartley patterns. It is important to note that there is no formula applicable to Fibonacci retracement levels.
A sharp rise or swings in volumes give the first sign of reversal and if this continues for a few more sessions, one can look weakness in the stock. The Fibonacci series is a sequence of numbers starting from zero arranged in such a way that the value of any number in the series is the sum of the previous two numbers. TPA (full form – Third Party Administrator) is a licensed interm…
What is the difference between Fibonacci retracement and extension?
Ans. As trading tools, Fibonacci retracements and extensions differ primarily in that extensions are frequently used to decide when to exit a trade. Retracements, however, are used to choose a favourable entry point and can also be used to formulate an exit plan.
So, the retracement, in this case, refers to the movement from the bottom . In this context, the Fibonacci retracement tool may provide insights into potential resistance levels if the market starts to move up. While technically not a Fibonacci ratio, some traders also consider the 50% level to have some significance, as it represents the midpoint of the price range. Fibonacci ratios outside of the 0-100% range may also be used, such as 161.8%, 261.8% or 423.6%.
Mastering Fibonacci Retracement
In short, the Fibonacci numbers have a relationship with nature. Moreover, you can find fantastic consistency in the ratio properties when a numerical in the Fibonacci series is divided by its following number. To completely comprehend the idea of Fibonacci retracements, you must understand the Fibonacci series. No need to issue cheques by investors while subscribing to IPO. Just write the bank account number and sign in the application form to authorise your bank to make payment in case of allotment. No worries for refund as the money remains in investor’s account.
This series has an infinite number of terms, each of which is simply the sum of the two numbers before it. The fact that each number in this series is around 1.618 times bigger than the one before it is one of its notable features. Thanks but there is no such option to save.There is only one option which restores the defaults (which removes my added 78.6 % level). • Extension levels can be drawn on different price waves over time.
• If in a stock, a new high/low occurs, the trader can use the Fibonacci extension levels to get an idea of where the price can go. Angel One has created short courses to cover theoretical concepts on investing and trading. These are by no means indicative ironfx forex review of or attempt to predict price movement in markets. In the event that the price of a stock rises by INR 100 and then proceeds to fall to INR 23.6. In such a scenario, the price would have retraced by 23.6% which happens to be a Fibonacci number.
Once you spot a strong price move that starts to fade, simply attach the Fib levels by connecting the low and high of the initial move. The platform will show where the above-mentioned ratios are located on the chart. Index funds replicate the performance of a stock market index, such as the Sensex or Nifty 50 to ge… In order to find the retracement levels, you have to find the recent significant Swing High and Swing Low.
When it doesn’t pan out, it can always be claimed that the trader should have been looking at another Fibonacci retracement level relatively. These Fibonacci retracement levels present a good opportunity for the traders to make new positions in the trend direction. As per the theory of the Fibonacci level, after the up-move, you can anticipate a correction in the stock to stay up to the Fibonacci ratios. For instance, 23.6% could be the first level the stock can correct.


I don't know about the rest of you, but for a "short" work week, it seemed to be very long and I am SO glad it's Friday!
And if it's Friday, that means there was a weigh in this morning. I've lost another 2 pounds this week, bringing the total to 12.
I was a LITTLE disappointed that it wasn't more this week, since my first few weeks are usually the biggest, but I am happy with ANY loss. And then I start playing the math game - if you lose 2 pounds a week for 10 weeks it's 20 pounds and if you do it for 20 weeks, it's 40 pounds.
So for now, I am going with the "multiplication theory of weight loss" in my head and that makes me happy.
Have a great weekend everyone!


When all of the partials (component frequencies) in a complex tone are all integer multiples of the same fundamental frequency, the sound is said to have a harmonic spectrum. Each component of a harmonic spectrum is called a harmonic partial, or simply a harmonic. The sum of all those harmonically related frequencies still results in a periodic wave having the fundamental frequency. The integer multiple frequencies thus fuse “harmoniously” into a composite harmonic wave form and is perceived by the human ear as a single tone.
In the middle of the nineteenth century, the German physician and physicist Hermann von Helmholtz (1821-1894) recognized that a musical tone conveying a clear sense of pitch must have several strong harmonic overtones in order to create a harmonic spectrum. Writing on the sensation of tone, he pointed out that tones with a moderately loud series of harmonics up to the sixth partial sound rich and musical. 1
All instruments in today’s modern orchestra generate complex tones however, not all vibrate with harmonic motion and therefore do not create harmonic partials or create a composite harmonic wave. A good example would be the sounds emitted from cymbals or gongs, which are definitely complex tones but they are not all harmonic. Timpani do not generate harmonic partials either yet they are considered to be a “pitched” percussion instrument.
Of the orchestral instruments that do generate a harmonic spectrum and create a composite harmonic wave (strings, brasses and winds etc.), we hear various pitches according to whether a string or column of air is vibrating as a unit through its whole length or in particular fractions of it. The vibration along the whole length of a string or column of air gives the lowest or fundamental tone. The vibrations taking place at various fractions of the length produce higher pitches called harmonics or upper partials. The stationary points along a string or column of air (i.e., where the waves cancel each other out) are called nodes or nodal points.
In mathematical terms, the frequency of each harmonic is in inverse proportion to the size of the fraction. This means that the vibration of equal halves of a string or a column of air produces double the frequency of the whole (and thus sounds an octave higher), the vibration of equal thirds triples the frequency (and therefore sounds an octave and a fifth higher than the fundamental note) and so on. The range of notes produces what is called the harmonic series or overtone series.
The examples in the next section show what the harmonic series looks like when it is notated in traditional musical staff notation and what the individual partials sound like. There is also a sound clip of what a harmonic series sounds like when all of the harmonics are added together. Follow the notes on the grand staff as you listen to each sound clip. Listen closely to the intonation of each partial, especially as they progress higher on the grand staff. Each note or partial you hear is a simple sine wave.
Pages: 1 2


This calculator is a dependable and practical tool that is perfect for performing all kinds of calculations. Its user-friendly design, variety of functions, and durable construction make it a must-have for anyone who needs to make quick and accurate calculations on the go.
The calculator is an essential tool for anyone who needs to perform basic or complex calculations quickly and accurately. This calculator is designed to be user-friendly, with a clear and easy-to-read display and intuitive buttons for efficient operation.
It features a sleek and compact design, making it easy to carry in your pocket or bag, and is powered by a reliable and long-lasting battery. The calculator has a variety of functions, including basic arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced functions such as square root, percentages, and memory storage.
The calculator also has a durable construction, with a sturdy body and buttons that can withstand heavy use. Whether you're a student, professional, or simply need a reliable calculator for everyday use, this product is an excellent choice.


April 29th- May 4th- Book Fair (our shopping day is Thursday)
May 3rd- PAWS Meeting, Trash for Cash Collection
May 4th- Breakfast with Mom
May 8th- Art and Science Show (Kona Ice Truck will be here!)
May 9th-Farm Fit (brown bag lunch and drink)
May 17th- wear blue mission t-shirt
May 23rd- Field Day
*Please check Smart Snack Guidelines on the school webpage.
*Remember to watch for class Dojo messages on your email.
Your child may want to bring in a sweatshirt or sweater to keep in his/her locker as our room stays very cool.
Week of April 30th-May 4th (Unit 29, Two of Everything)
Target Skill- Understanding Characters, Point of View
All tests now online - (unless Chromebooks are being used for upper grade testing) *This week's tests will be paper/pencil due to ISTEP testing
This week our grammar skill will focus on possessive pronouns. We will work on persuasive writing.
Spelling List (Week of April 30th-May 4th )
1. aim 11. bright
2. snail 12. fright
3. bay 13. tray
4. braid 14. try
5. ray 15. below
6. always 16. saw
7. gain 17. something
8. sly 18. thought
9. chain 19. both
Basic word test on Thursday
**Sitton spelling words are # 15-19 on list.
Our current unit will focus on measurement. We will learn about customary units of measure. We will finish up learning about metric units of measure and take our test midweek. Next we will look at measuring capacity in cups, pints, quarts, and gallons. We use the X-tra Math computer program to help us practice our basic math facts. We work once a week on the Accelerated Math program. Each child works at his/her own level and at his/her own pace in this program. We use the Math Facts in a Flash computer program to work on memorizing/speed of our addition and subtraction facts.
This week we will go back to Social Studies to cover a unit on cultures and traditions. We have a consumable Science book with our new Science series this year.
Chapter 4- Celebrating Our Traditions
Lesson 1- Culture Is Our Way of Life
Lesson 2- Cultures in Our Country
Each week we will follow the A, B, C, D, schedule for special classes.
A- P. E.
We will have A, B, C, D, then repeat. It would be a good idea to keep a pair of tennis shoes in your child's locker so that he/she will be prepared on P.E. days.


The focus of the COMPUTAL project is on the following related topics: computable analysis, domain theory, topology, and exact real number computation, hereby dealing with both theoretical and applied aspects.
A major motivation for undertaking this research is the fact that in safety-critical applications it is not sufficient to produce software that is only tested for correctness: its correctness has to be formally proven. This is also true in Scientific Computing. The problem here is that the current mainstream approach to numerical computing uses programming languages that do not possess a sound mathematical semantics. Hence, there is no way to provide formal correctness proofs.
The reason is that on the theoretical side one deals with well-developed analytical theories based on the non-constructive concept of a real number. Implementations, on the other hand, use floating-point realisations of real numbers, which do not have a well-studied mathematical structure. Ways to get out of these problems are currently promoted under the slogan “Computing with Exact Real Numbers”. Well developed practical and theoretical bases for exact real number computation and, more generally, computable analysis are provided by Scott’s Domain Theory and Weihrauch’s Type Two Theory of Effectivity (TTE). In certain applications also other computational models are used. Moreover, strengthening the underlying logic has been suggested. The full relationship of these approaches is still under investigation.
Weihrauch’s TTE is based on Turing machines that by computing infinitely long transform infinite strings. The study of such computations is important also for other branches of theoretical computer science including specification, verification and synthesis of reactive systems as well as stream computability. In contrast to the theory of finite computations, the study of infinite computations crucially depends on topological considerations.
Constructive approaches have the important property that correct programs can be derived from formal proofs.