HomeArticlesSingle and double angle plots interpretation for Astigmatism Analysis
Single and double angle plots interpretation for Astigmatism Analysis
October 13, 2019
There are two ways of representing the results of astigmatism analysis The first way is the most common way that everyone knows because it is the way That is more common or more familiar with the real location around the eye It is the Single Angle representation. In this kind of Single Angle representation We have a polar plot from 0 to 360 degrees and we know that the zero is the same location that the 360 degrees and that are coincident with the locations in the eye. Anyway when we work with astigmatism analysis the most common and the most adequate could be to work in a double angle even though we can show all the results in a single angle plot. All our calculations are going to be performed in a double angle plot and in the next lesson We will explain what is the reason of this kind of analysis based on the double angle. The most important here in order to interpret correctly the result is that if we are working with a single angle if our results are representing in a 360 degrees plot, our results are going to be classified in with-the-rule astigmatism in the vertical orientation. You can see here that the blue area is the area that contains all the cases that are with-the-rule cases with-the-rule astigmatism and we have the against-the-rule in the horizontal location Also we have this kind of oblique locations in yellow. Anyway, This is very familiar for the surgeon because you see exactly what are the locations of the astigmatism in the same way that are located in the real eye. Anyway if you have a double angle plot you have to see first What is the number of angles you have in the plot You can see here that you have from 0 to 180 So the data are going to be represented in a different way. All your with-the-rule cases are going to be located at the left side of the plot and all there against-the-rule cases are going to be located at the right side. So in the vertical locations you are going to have the oblique positions So you have to know before to interpret the results If you are working with that single angle or if you are working in a double angle plot. Even though you can represent in both sides you can see here exactly what is the corneal topography for the different kinds of astigmatism. E ven though you can use both plots. Always the calculations are going to be conducted in a double angle plot and later you have to transform the location of the points to a single angle if you want to represent a single angle and usually If you are going to represent in a single angle you are going to represent only the upper side of the plot. Not all the plot like in the double angle because here you have one hundred and eighty degrees and here You have also one hundred and eighty degrees.


Algebra IS Useful... Right?
Why do so many of us dislike algebra?
I think it’s fair to say that most people aren’t too fond of algebra, to put it mildly. Why do so many students, and adults for that matter, react to algebra the way Superman might react to Kryptonite? Perhaps part of the reason why so many people think that algebra is boring, or confusing, or just plain incomprehensible, stems from the way they were taught (or, as the case may be, “taught”). Often, algebra is presented as “Rules That Must Be Followed Unthinkingly and Without Question”; what’s commonly missing from this approach is the why behind the rules. Without that “why”, it can be difficult to understand and apply those rules, let alone remember all of them. Imparting that “why” effectively is an art form, and a topic that is deep and important, deep enough that we wouldn’t dare try to address it in a quick blog post. Here, we are interested in a different kind of “why”: why should we teach algebra at all?
Is algebra really useful on the job?
Students are typically told that algebra will at some point be useful to them in their daily lives as adults, and that SO many people use algebra on the job, weekly if not daily! If you google “jobs that use algebra”, you will see websites galore listing all the many professions that use algebra. You will be told that nurses, plumbers, managers, and chefs all apply algebra in the workplace. Many people will tell you that algebra is used in almost every job there is! However, this is very, very far from the truth. Most people will never use algebra on the job, or in their daily lives off the job. That’s right, nurses, plumbers, managers, and chefs generally do not use algebra to do anything job-related or otherwise. And no, you will not use algebra when you go shopping. You might use arithmetic, but you won’t use algebra.
Who actually uses algebra?
That’s not to say that algebra isn’t important to our lives. It is incredibly important. Algebra is one of the essential foundations of elementary mathematics, which in turn serves as the foundation for advanced mathematics, which serves as the bedrock upon which the sciences, technology, and engineering are built. But it is incredibly unlikely that students will ever use algebra, for any reason, in their future careers. And even the people who you think might use algebra all the time, like engineers and scientists, use software to do whatever algebra is necessary for them. They are generally not writing out the quadratic formula and solving supposedly “applied” problems about speeding trains about to collide.
So, why do we learn algebra?
So why do we kid ourselves about why we learn algebra? Why do we, well, lie to our students about how algebra will be a fixture in their future jobs? Just to give them a reason to foist it upon them, it seems! I think we should be honest with our kids. We learn about algebra for the same reason we learn about Shakespeare: to enrich our intellectual lives. And certainly that’s what Shakespeare does, for many people, for many different reasons. But algebra is a different beast entirely. Algebra can teach something that Shakespeare has a much more difficult time getting across: algebra teaches us how to think logically.
Because algebra teaches critical thinking!
Algebra, and mathematics more generally, is the training ground for logical thought. It’s about understanding procedure and process, and where these come from and why. It’s about applying methods and algorithms in a deliberate and thoughtful manner. It’s about being consistent, and yes, following rules unquestioningly, but only after you have questioned them thoroughly. These are skills that our students need to practice and master for their future jobs: how to understand a problem, break it down into its constituent parts, and find a solution using those parts in a logical and step-by-step fashion. Algebra helps to train your brain, and once you have that training, you can apply these ideas to problems that are not algebra. And that’s the really important part.
Our kids don’t need to know a lick of algebra to excel as an architect, businesswoman, or doctor. But they do need to know how to apply the habits of mind and critical thinking techniques that a thorough study of algebra can provide. And not only is that incredibly practical, but even better, it’s the truth.
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Basic Business Math for Installation and Design Professionals
An understanding of basic mathematical principles is important for any business person. Math skills enable you to figure out resource requirements, estimate costs, work out average time spent on different activities, and calculate commission earnings. The ability to analyze and comprehend numbers is a vital skill for personal, as well as corporate, growth and success. This course builds on the basic math skills that you learned in your school years, showing you how to apply those skills to some common business situations. And it helps you to confidently use whole numbers and decimals in business through a series of real-life problems and examples.
Why you should attend?
Learn how to apply basic math skills to common problems
What to expect?
All BICSI CONNECT courses require an internet-capable device and internet connection.
Java software; Windows 7 or 8; Mac OSx10.6+; Android 4.1 or later; Apple 10S 6.x, 7.x; IE 10 or later; Firefox 21 or later; Chrome 29 or later; Safari 5.1.8 or later; sound card with speakers/headphones for audio (audio not available for all courses); pop-up blockers disabled.
Who should attend?
This course is ideal for all iCT professionals
What will I learn?
After this course you will be able to:
- Estimate using rounded whole numbers in a given
- Identify the characteristics of whole numbers
- Identify which fractional amount is the largest when
comparing a simple fraction, a percentage, and a ratio
- Put fractional amounts in order from smallest to
- Add and subtract decimals to solve business problems
- Multiply and divide decimals to solve business problems
How long is this course?
One-hour self-paced course available for 90 days from the date of purchase
Can I earn credit?
Earn 1 Continuing Education Credits (CEC) upon successfully completing this program.
What is the cancellation policy?
All BICSI CONNECT courses are nonrefundable and nontransferable


I,shirsha Chowdhury,was under Aloke Sir's guidance in 'IIT Maths Wizard' during my IIT/WBJEE preparation.Sir's teaching method
is very unique,as he Starts from a very basic level and then reaches advanced level. He tought us many logical approaches so as
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advanced Mathematics. Joining Sir's classes helped me a lot in improving my concepts and getting a good grasp of all the topic.
i would recomended all my juniors to join Sir's classes as it would improve their concepts as well as problem solving skills for
various competitive exam.


Assessing the square footage of a home is not so difficult, but it involves some legwork, record keeping and mathematics. Understanding how big a residence is helps in estimating how much it will cost to heat or cool it, also it is an essential item of advice when thinking about selling or leasing the home. Insurance companies will want to learn how big the home is.
Draw an image of the property’s outline . Single-family homes are easier to quantify outside. Width and the length of the home need to be measured.
Put the tab of the tape measure on one corner of the home and pull it until you arrive at the opposite side. This task is easier with two people, one to hold the tab in place and the other to assess the length of the wall. In case your tape measure isn’t long enough to reach the other side, make a little mark with the pen on the wall and then write down the dimension up to there on the paper drawing of the property’s design.
Repeat these steps until width and the length of the home have been noted. Add up the feet of both wall crosses individually, and around any fractions up to another inch. Convert the measurement to feet for both partitions. Multiply the length by the item, as well as the width will signify how many feet are at the home.
Quantify the floor just as for a home. In the event the second floor is exactly the same dimensions as the first floor, then just double click the square footage to obtain the square footage of the entire home.
By measuring the width and length of the upstairs, measure the square footage of the second floor from interior.
Add 4 inches into the ends of each wall as you quantify it to compensate for the width of each wall. Add up the duration for each span and total up them to find the actual width and length. Then multiply the totals to discover the square footage of the upstairs. Add it into the square footage for the first floor to obtain the total square footage of the home.


The integration of hand-held graphing technology (HHGT) in the teaching and learning of mathematics
Research questions include:
- What changes in learning and teaching are facilitated by the technology? What are the possible impacts on the curriculum, in assessment, and in pedagogical content knowledge?
- What is the current preparation of pre- and in-service teachers on the proper integration of HHGT?
- Teaching Mathematics Using Inquiry, Technology, Collaboration, Reflection, and Formative Assessment.
- The impact of HHGT in general, and of dynamic geometry software in particular, on the exploration and discovery of secondary students.


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What is it difference between complexity theory and chaos theory in computing and algorithms?
Does complexity theory equal chaos theory?
THE GREAT NAMAZU RETIRED JAPANESE DEMI GOD< TURNED ANALYST
Editor's Note 7/11/2016 Namazu and his pals at Helios Ruehls, Inc. go where no catfish has gone before ...across the Euculidian / Newtonian line. Watch the blog for periodic reports.
The short answer is no, but......what often appears as chaos is sometimes simply complexity we haven't met yet. Sometimes more accurate systems of measure of initial conditions may nudge a chaotic system into the complex realm. But there is a distinct difference between complexity theory and chaos theory and a difference in the computations and algorithms used and continuing to evolve.
Both theories and their related equations , computations, and algorithms are used to study systems that are non linear in nature. Uncertainty is a major characteristic of both chaotic and complex systems. The nature and origin of the complexity is the key difference between chaos and complexity.
Note that the term “edge of chaos” gets used quite a bit in scientific and science fiction writing. Confusing the matter, this term is normally associated with complex systems. "The Edge of Chaos" represents a point that sits along a spectrum. On one end is determinism and on the other is not chaos per se, but randomness. The edge of chaos begins where there is sufficient observable structure / patterns in the system that it is not random, but also enough fluidity and emergent creativity that the system is not deterministic.
Patterns are an important,and often repeating element in complex systems despite the fact that complex systems have inherent uncertainty. With sufficient observable patterns and structure future actions, changes, within a complex system are not random, but fall within a predictable range of possibilities. Complex systems are never "one right answer" systems they are nonlinear non-Euclidean. In the hey day of classical (Euclidean) math they were a source of great controversy. (See my post "August 10, 1632 THE BATTLE OVER THE "INFINITESIMAL" ) The emergence of complexity theory demonstrates a domain between deterministic order and randomness which is complex. Complexity Theory did emerge from Chaos theory but it does not eclipse Chaos theory. Chaos is sometimes perceived as extremely complicated information rather than an absence of order. Chaotic systems, in contrast to complex systems, remain deterministic. Their long term behavior can be practically impossible to predict with any accuracy.
When one engages in analysis of complex systems,sensitivity to initial conditions , if even knowable, is not as important as within systems contained in Chaos Theory. Initial conditions are a primary consideration within Chaos systems where sensitivity to initial conditions, prevails as a deterministic element.
.In Conclusion, it can be tempting to think of of Chaos theory as a theory of highly complex types of complex systems. But that is not the case Chaos theorists have contributed some key insights of complexity, like sensitivity to initial conditions, but Chaos Theory remains a study of deterministic systems. To understand non-deterministic systems, like ant colonies , or markets, it’s necessary to look at complex systems and Complexity Theory.


In my conversations with some of my statistics colleagues who are less familiar with Bayes methods, I came up with four categories of problems that come up in Bayesian-Frequentist comparisons.
Conditional probability problems
An example of this is
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
There are a million of these sorts of questions, and I did about 5-10 of the questions from the actuarial P test. Clearly the use of Bayes Theorem is essential in all of this, and is uncontroversial on these problems - there really isn’t an alternative. If you dislike the term "Bayesian" here, as some textbooks seem to, you can refer to these as conditional probability problems but we're talking about the same thing. So, the difference between so-called Orthodox or Frequentist approaches and so-called Bayesian approaches to problems must lie in other types of problems. I'll note that intro stats books of all stripes include these problems, and from a Bayesian perspective they are typically limited to these types of problems.
Sampling distribution of the mean
My first encounter with the difference between Frequentist and Bayesian perspectives was in the "sampling distribution of the mean” chapter. The problem, say, is given a series of measurements of something (i.e. the mass of Saturn, the lengths of flower petals, etc…) what is the best estimate for the underlying quantity - e.g. what is the best estimate of the mass of Saturn and how confident are we in that measurement? Say, from orbital data, we get the following 10 data points for the mass of Saturn (in Earth-masses):
102, 95, 85, 86, 93, 105, 96, 91, 104, 115
What is the best estimate for the mass of Saturn, and our uncertainty in that estimate?
Both Frequentist and Bayesian methods come up with
The Bayesian and Frequentist approaches will come up with - numerically - the same answer to this question, but the vocabulary will be different. One speaks about the probability of the mean value, the other about the properties of the sampling distribution with respect to \(N\) data points. In either case, it makes no difference practically.
Jaynes-type Galilean problems
Where the rubber meets the road is a problem like the one proposed by Lindley, where he flipped a thumbtack and noted that sometimes it lands "point up" and others “point down”. His actual data was:
U U U D U D U U U U U D (9 Ups, and 3 Downs)
And the question is, can we be 95% sure of this tack being an unfair tack? Given the physical properties of thumbtacks, we really don’t have any expectation that it should be fair (unlike a coin, where we have a symmetry argument). We come up with different answers - quantitatively and possible qualitatively - on this one (see page 54 of the presentation on the three-sided coin I gave)
Anything with the Cauchy distribution
There is one final category of problems in the comparison with Bayesian and Frequentist methods.
Imagine we have a lighthouse which is off shore some known distance, B, and is located along the shore at some unknown location \(x=a\):
(lighthouse) * --- ^ | B | V ————shore——————+——————————————————————> x x=a
we want to estimate the location (“a”) from a series of locations of flashes on the shore - the lighthouse is spinning around and flashing at random times. We can only observe where the flash lands on the shore, not the direction it came from. The data is, for example, the locations of these 10 flashes:
-4.89, 1.03, 1.64, 1.17, 0.74, 1.46, 0.76, -7.16, 0.31, 2.48
One can show that the location of a single flash should follow a Cauchy distribution: \(p(x|a,B) = B/(B^2 + (x-a)^2)\). This is due to the angular geometry of the problem.
The question is, what is the best estimate of “a”? What is the uncertainty in this estimate? What methods would you employ? The Bayesian treatment for this problem is in D.S. Sivia’s, Data Analysis: a Bayesian Tutorial, Second Edition (Oxford, 2006). A very similar problem is given in Think Bayes and another nice treatment is on João Pedro Neto's blog.
I'm pretty sure this problem is resistant to any procedure relying on sampling distributions (as all Frequentist procedures are) due to the peculiar properties of the Cauchy Distribution.
It is important when discussing different perspectives to keep clear what the vocabulary is - what are we actually talking about? If you limit the problems to simple conditional probability problems, there isn't any difference between the Bayesian and Frequentist perspectives and one might wonder what the big deal is? However, if you expand the problem set to include limited \(N\) problems, with non-Normal distributions (such as Beta and Cauchy), then the differences start to become apparent.


Algebra Rule 5
Fractions can be summed by multiplying across between numerators and denominators, and multiplying denominators for a common denominator
If top and bottom of a fraction are both multiplied by the same number, the fraction remains unchanged. So, we can sum two fractions by first multiplying each fraction's numerator and denominator with the other fraction's denominator. Then, since both the fractions now have the same denominator (the product of the two denominators), we can combine them into one fraction, with the sum in the numerator.


I wrote the following in response to a class I just taught on arguments for the existence of God. A student asked about what happens to the strength of probabilistic arguments when they are combined. Bayesian reasoning often shows us that the likelihood of something being true given our evidence is lower than we think. In this post, however, I examine what happens when we have multiple lines of converging evidence, which often turns out to raise the probability higher than we might guess.
I thought I would write up a brief further explanation of this kind of probabilistic reasoning since it came up in class, and it seemed that most people were unfamiliar with how to think through such problems. (Human intuition is actually really bad at guessing probabilities, which is why pro poker players can clean you out.) It’s also pretty hard to understand without seeing it written out.
Suppose you go in for a cancer screening and the doctor brings you the unfortunate news that the test is positive. Suppose he also tells you the following facts:
- Only 1% of people in general have cancer.
- If someone has cancer, the test gives a positive result 80% of the time.
- If someone does not have cancer the test gives a false positive 10% of the time.
What are the chances that you actually have cancer? Seems pretty scary, right? Wouldn’t you guess that your chances are pretty high? The answer, however, is that they aren’t actually that high at all.
Call the probability that you have cancer P(C), and the probability that you have cancer given the positive test result P(C|T).
P(C|T) = P(C)P(T|C)/P(T)
In plain English, this means that the probability you have cancer equals the proportion of true positive test results divided by the total positive test results including all the false ones. This last bit is the crucial thing to see. There are actually many many more false positive test results than true positive test results even though the false positive rate is only 10% and the true positive rate is 90%.
Why is this? It happens because its so unlikely that you have cancer in the first place. Let’s do the math.
True positives = 1% * 80% = 0.008.
In a population of 10,000 people 1% have cancer, so that’s 100 people. If all of those took the test, 80 of them would test positive.
But how many people would test positive who don’t have cancer?
False positives = 99% * 10% = .099.
In a population of 10,000 people 99% don’t have cancer, so that’s 9,900 people. If all of those took the test, 990 would test positive.
So given that you have a positive test result, what are the chances that you are in the first group rather than the second group?
Well, we take the ratio of the true positives by all the positives, which equals,
80/(80+990) = 0.747663
So you have a roughly 7.5% chance of having cancer given the test result. Surprisingly low right?
Now here’s the real zinger regarding converging lines of evidence that I explained to Micah above in abbreviated fashion. Suppose that you took a second test with similar numbers:
- If a person has cancer, then test 2 gives a true positive 90% of the time.
- If a person does not have cancer, then test 2 gives a false positive 10% of the time.
Unfortunately, this second test also comes back positive. What are the chances that you have cancer now? You might think that it’s just the union of the two probabilities P(C|T1) ∪ P(C|T2), but you would be wrong. That number would actually be way too low, now. (That comes out to 15.18% if you’re curious.)
The trick is to see that given the first test result you have to update the likelihood that you have cancer from 1% likely to 7.5%. (The other, shorter but less intuitive way is just to do an additive version of the Bayes’ Theorem.)
So now we go through the same steps we did above, but instead of multiplying 1% * 80% to get the number of true positives, we have to multiply 7.5% * 90%, which is obviously much higher. We also need to lower the number of false positives. Instead of multiplying 99% * 10% we are now multiplying 92.5% * 10%.
When we run the numbers, we get a result of approximately 42.2% likely that you have cancer given two separate positive results. Interestingly, it is still more likely than not that you don’t have cancer because of how rare cancer actually is, but that second number is way higher than you might think given the low likelihood of either test result independently indicating that you have cancer. This is the power of converging lines of evidence. You can see that if we add a third and fourth test, this likelihood would shoot up pretty fast.
Similarly, lines of argument that on their own only raise the probability of God’s existence slightly can combine to make a very powerful total case, just like multiple pieces of evidence in a trial, provided that they are actually independent pieces of evidence and not just recycling the same evidence in a circular fashion.


Classic Betting Strategies - The Fibonacci System
Leonardo Fibonacci, born in Pisa, Italy in the 12th century, actually got his last name after he died. Fibonacci is a sort of a nickname. He earned fame as an outstanding mathematician. He introduced Hindu-Arabic numerals (which is what we use today) to Europe, which replaced the cumbersome Roman numerals in use at that time. 더킹카지노 Can you imagine multiplying two Roman numerals together? How would anyone calculate the answer to CXIV times LXII? I don't know how the Romans built their fantastic structures with such a severe mathematical handicap.
Fibonacci used a number series, which had been developed hundreds of years earlier, to solve some mathematical problems, and today that series bears his name. The first two numbers of the series are zero and one. Each subsequent number is determined by adding the two previous numbers together. The series becomes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so forth. (In some versions the initial zero is omitted.) Recently this number series gained notoriety as the 10-digit bank account number in The DaVinci Code book and movie. Some investment gurus derive ratios from the Fibonacci series to help with financial market analysis by identifying key levels of support and resistance.
How do we use this series as a gambling strategy? First modify the series by eliminating the first two numbers, zero and one. Then start with a bet of one unit. If you win, bet one unit again and keep on betting one unit until you lose. After a loss, increase your bet one level and continue increasing one level after a loss but reduce your bet one level after any win. If you win two bets in a row or two bets out of three, drop back to the first bet in the series.
You have to have a strong stomach for this system since you will get up to the higher numbers once or twice in every hour of play, but if you stick it out, the system performs very well. I would also recommend starting over if you lose five bets in a row to avoid serious damage to your bankroll. For the same reason I also wouldn't go any higher than the 34-level.
If you play with a partner, you can bet on the opposites. For example, one bet always on black and the other always bet the red. Surprisingly, you may both end up winning.
by vofos on 2020-07-23 11:14:48
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|Series||Mathematics towards relevance|
|Contributions||Working Mathematics Group.|
|The Physical Object|
|Number of Pages||48|
Download Maths and the telegraph pole.
“Maths and the Telegraph Pole” tells the story of the hard sums that people who put up telegraph poles have to do, in their heads, all the time holding on to lengths of wire.
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A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to.
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Answer this question and win exciting prizes. Working Mathematics Group: Maths and the Telegraph Pole: Tutor’s Notes, Uckfield, Working Mathematics Group, Understanding Interest (Mathematics of Finance 1) (with video), Working Mathematics Group, Living with Interest (Mathematics of Finance 2), Revision definition: To make a revision of something that is written or something that has been decided means | Meaning, pronunciation, translations and examples.
Brooklyn, New York, United States About Blog Book Riot is a blog covering book-related news, reviews, commentary, advice and information along with the latest in book-reading books.
Never boring. Frequency 4 posts / dayAlso in Literary Blogs Blog Facebook fans K ⋅ Twitter followers K ⋅ Instagram Followers K ⋅ Domain Authority 80.
Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory. Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory.
Distance travel by train to cross pole = Length of train = m Time =distance / time = /40 = sec Q A train covers a distance of 12 km in 10 minutes.
If it takes 6 seconds to pass a telegraph post, Find the length of the train. Solution: Time = 10min = 10 x 60 = sec, distance = 12km = m Speed of train = m/sec = 20m/s.
The comedian and television presenter Michael Palin has praised the study of geography as a force for broadening the mind as fresh figures show a spike in take-up for the subject at schools in. On the crest of a distant hill, a single telegraph pole stood slanted against the sky, like a cross over a vast grave.
It took them three hours and a punctured tire to crawl in low gear through trackless soft, through gullies, then down ruts left by cart wheels—to reach the settlement that lay in the valley beyond the hill with the telegraph.
Name the ceremonial folk dance performed around a tall pole garlanded with greenery or flowers and often hung with ribbons that are woven into complex pattern by the dancers: Answer: Maypole dance.
Identify the number of sons of Karamchand Gandhi: Answer: 6. At the latest definition: You use at the latest in order to indicate that something must happen at or before a | Meaning, pronunciation, translations and examples.
This is the aptitude questions and answers section on "Problems on Trains" with explanation for various interview, competitive examination and entrance test. Solved examples with detailed answer description, explanation are given and it would be easy to understand.
NCERT Solutions For Class 10 Science Chapter 13 Magnetic Effects Of Electric Current: In this article, you will find out all the necessary information regarding the magnetic effect of electric current class 10 NCERT the students who are in search of NCERT Solutions For Class 10 Science Chapter 13 Magnetic Effects Of Electric Current can refer to this article.
General Knowledge 31 – 31) Which country has the world’s one-fourth oil reserve. Answer: Saudi Arabia. 32) What is the old name of Taiwan. Answer: Formosa. 33) Which is the dangerous mark of the Richter scale which records earthquake.
Answer: 6 and above. 34) Which is the largest internet complex of America. Answer: America On-line. Book Description. Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a popular reference book for designers of heavily loaded composite updated to mirror the exponential growth and development of composites, this English-language Third Edition.
Contains all-new coverage of nanocomposites and biocomposites. For answering these types of questions just consider 2–3 points Firstly to cross the pole train has to cover its whole length So total distance covered = length of the train Second point is you have to see the units are same or not Here distance i.
Selina Solutions Concise Mathematics Class 6 Chapter 17 Idea of Speed, Distance and Time Exercise 17(B) provides clear answers of problems mentioned in. See what your friends are reading. Sign up to see what your friends are reading, get book recommendations, and join the world’s largest community of readers.
Titled The Social Network, it is based on a book, The Accidental Billionaires, by Ben Mezrich, for whom "this is the ultimate geek-becomes-success Author: Elizabeth Day.From Longman Dictionary of Contemporary English telegraph tel‧e‧graph 1 / ˈteləɡrɑːf $ -ɡræf / noun 1 [uncountable] TCT an old-fashioned method of sending messages using radio or electrical signals 2 [countable] TCT a piece of equipment that receives or sends messages in this way — telegraphic / ˌteləˈɡræfɪk / adjective.Stephen Hawking was the Lucasian Professor of Mathematics at the University of Cambridge for thirty years and the recipient of numerous awards and honors including the Presidential Medal of books for the general reader include My Brief History, the classic A Brief History of Time, the essay collection Black Holes and Baby Universes, The Universe in a Nutshell, and, with Leonard /5().


This extra-large set stimulates participation in creative construction, sorting, counting, basic operations and problem solving activities. Develop important skills in color and pattern recognition, spatial relationships, logical reasoning, and numeracy. Activities include making shapes, recognizing and building patterns, basic numeracy, and symmetry. The creative possibilities are endless with this monster pack. Designed to be tough, these blocks will easily stand up to the rigors of classroom use. Set includes 500 blocks (3/4" square) in 10 bright colors (400 cubes, 50 triangles, 50 quadrants), 4 base boards, and 42 double-sided activity cards. Everything stores in a sturdy plastic container (about 15" x 12" x 8").
WARNING: Choking Hazard - Small parts. Not for children under 3 years.


The Heroes Among Us
Charter School Associates
Recognized from Governor Rick Scott for top ten performance by Hillsborough Academy for Improvement in Mathematics Achievement! Way to go!
Power School Log on
CONGRATULATIONS Hillsborough Academy of Math and Science on Earning an "A" School Grade!!
“I am very happy to have discovered HAMS, totally happy with all the school has to offer.
“This is an awesome school. I have 3 kids and all of the teachers across all grade levels are awesome. HAMS Parent
“I am very excited for next year's field trips. This year's were a blast!
“This school is amazing! The teachers are well trained and professional. The principal is devoted and easily approachable. The curriculum is challenging and the students have fun! Greatest school on the planet!. HAMS Parent
“This is a great school! They have accomplished amazing things.
I am glad to have been a part of this school since the beginning.HAMS Teacher
“After attending another school in the area and not getting the help my daughter needed I decided to transfer her to HAMS. Within the second 9 weeks she was able to get honor roll.. HAMS Parent


Semigroup theory, and subsequently inverse semigroup theory, is a broad field that is part of many different areas due to its generality. For example, it can be found in parts of computer science, more specifically the concepts of finite state automata and the study of formal languages.
This paper shall discuss the history of the field, and then we shall discuss some basic definitions of groups and semigroups to lay the foundations needed for the rest of this report. From there we will discuss the partial order, which is a concept that arises often in regards to semigroups and inverse semigroups. Then we shall discuss some well-known theorems, namely Cayley’s theorem, an important theorem for groups, and the semigroup analogue in the faithful representation theorem for full transformation monoids.
After this we shall discuss inverse semigroups, explore the natural partial order, which is a partial order restricted to E(S) which works very nicely in inverse semigroups. Then this will lead us to discussing symmetric inverse monoids and the Wagner-Preston representation theorem which is the inverse semigroup analogue to Cayley’s theorem.
paper some examples will be discussed for each of these sections, as well as a couple of
fleshed out examples, namely the Sierpinski triangle and the bicyclic monoid. The aim of
this paper will be to present these concepts so that the groundwork is there to pursue
deeper research into this topic.


Download the following files:
The daily_prices file contains stock ticker symbols and opening, high, low and closing prices, as well as sales volumes.
The dividends file contains stock ticker symbols and dividend amounts.
Only a subset of stocks have dividends, so the stocks in the files do not match one-for-one.
Line one of each file is a header row that shows which column is which.
For every stock that pays a dividend, calculate the Market Capitalization (volume * closing price) for each day at the stock market’s closing bell. Identify which dividend-paying stock had the highest Market Capitalization of them all.
By way of example, based on the samples below, NGI and NAV are dividend-paying stocks, but NEX is not. Calculating the Market Capitalizations (MC) for NGI and NAV, the highest MC is NGI’s with an 200592, thus the answer is NGI
35.05 * 5500 = 192774.9
35.02 * 5400 = 189108.0
41.22 * 3900 = 160758.0
41.64 * 4800 = 199872.0
41.79 * 4800 = 200592.0
SAMPLE prices file:
SAMPLE dividends file:


I've published my first app: "Play Your Cards Right". It's is a very simple 1 player card game I mainly built to learn the first priciples of android app development. 6 cards are drawn at random, the first is shown to the player who is invited to guess if the second is higher or lower. If they guess correctly the third card is shown, and so on until they either guess incorrectly (they lose) or all the cards are revealed (they win); you get nothing for a pair, not in this game; and aces are high.
The game is based on Bruce Forsyth's 80s classic of the same name:
The game has also been adopted by my local pub—The Herne Tavern—as the climax to its famous Sunday night quiz hosted by TV's Pietro Herrera: http://theherne.net/. As such, my App might be a useful practice tool for The Herne's loyal quiz goers.
Although simple, it's a fun game and the win rate is much lower than you'd expect. My rusty statistical skills have thus far proven inadequate for calculating the theoretical probability of winning a game given the player always makes sensible choices. However I previously built a php web version here: http://dean.xtsl.net/tools/cards.php (thanks Simon!) and a means to ask Simon's machines to run through a number of simulations of the game based on some simple stratergies here: http://dean.xtsl.net/tools/cards/simulate.php
Current ideas for version 1.1 include: A log of results, and hints.
Thanks and good luck beating the game!


Calling All Learners from Kindergarten to Grade 6! Join us for our FREE event Jump 2 Math.
Get out, get moving, and learn math while having fun!
Date: Tuesday, March 26, 2019
Time: 6:00 PM -8:00 PM (Drop in Event)
Location: AAG Auditorium
Jump2Math is a kinesthetic, multi-sensory approach to teaching math that incorporates physical exercise, cooperative learning, and life-sized math board games, giant manipulative, and colourful activity math mats. Enjoy an evening out as a family and enjoy the fun! Parents who attend will receive access to a free portal to support math learning at home.
View videos of this interactive math experience below:
Learn more about Jump2Math by visiting: https://jump2math.ca/about/
Brought to you by AAG School Council and PROGRANT funding


Here's a problem Lewis Carroll enjoyed posing to kids like Alice: how many colors do you need to fill in any map so that neighboring countries are always colored differently?
It sounds simple enough. But when a Victorian law student first posed the question, guessing that it could be done with a mere four colors, logician Augustus De Morgan was stumped. While no one could devise a map that required more, a proof that every map requires only four colors proved remarkably elusive. Mapmakers didn't care, but problem-solvers were obsessed for decades, including the Bishop of London, a Kentucky colonel, and a California traffic cop. The question's very intractability has inspired innovations in computing and network theory, but some say it still has no satisfying solution.
Oxford professor Robin Wilson's Four Colors Suffice: How the Map Problem was Solved (Princeton: 2003) presents the colorful history of this conjecture, with an unassuming lucidity that will appeal to the mathematical novice. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride: after telling his class that the problem had been wasted on third-rate minds, the great number-theorist Herman Minkowski took weeks at the blackboard trying to solve it, finally admitting, "Heaven is angered by my arrogance; my proof is also defective."
The first dead-end occurred shortly after the problem was first posed in 1852. De Morgan became obsessed with his initial insight that in any group of four regions, each bordering every other, one region must be completely enclosed by the others, and thus safe from forcing any colors outside the group. Though undeniably true, this was a false start: looking at single groups of four, one at a time, fails to take into account the myriad ways these groups might interact in ways that force the use of more colors.
The next failure, which convinced mathematicians worldwide for over a decade, actually took giant steps in the right direction. Cambridge mathematician Arthur Cayley revived the problem in 1878 and suggested a totally new approach: if you assume there exist some maps that need more than four colors, and of those you take only the ones that have as few regions in them as possible, then you'll have a manageable but complete set of counter-examples on your hands. (Wilson calls these the "minimal criminals.") If you can show that none of these counter-examples can possibly exist, then you've shown that four colors suffice. The only problem is, there are lots of them.
London barrister and amateur mathematician Alfred Bray Kempe ran with this approach, devising an elegant method that claimed to cleanly dispatch with all possible counter-examples. He put one region after another at the center of a counter-example-first a two-sided shape, then a triangle, square and pentagon-then ruled them out by listing all the possible chains of regions that could branch off from them. The proof was widely accepted, and Kempe was elected a Fellow of the Royal Society, and even knighted.
But in 1890, Percy Heawood, an Oxford eccentric known for his immense mustache and flowing cape, produced a map that showed that one of Kempe's chains didn't work. Even as he disgraced Kempe, however, Heawood demonstrated the lasting value of his contribution, giving a full Kempe-style proof that five colors suffice. (As a result of Heawood's later work, we now know that any map drawn on a doughnut requires no more than seven colors, not counting sprinkles. "There are, of course, additional reasons why one seldom encounters a map of the United States on one's doughnut," mused novelist Tom Robbins.)
The modern story picks up in 1948, when German geometer Heinrich Heesch realized that if he could find a master set of patterns that can't appear in a minimal criminal, he would rule out all possible counter-examples and have a proof. But finding these patterns was really hard, and there were thousands of them.
Enter the computer. In 1976, after 2000 machine-hours at the University of Illinois, Kenneth Appel and Wolfgang Haken found every single one, turning out the first famous computer-aided proof. Some claimed this was not a proof, since it cannot be verified in detail by a human being. By admitting computer proofs into the canon, writes Robin Wilson, math was "in danger of becoming an empirical science, as fallible as physics." Far from a feat of pure reasoning, the answer appeared to some as a monstrous coincidence.
There's an unwritten law as old as math itself: proof comes with understanding. But Appel and Hanken's proof, while almost certainly valid, doesn't clear anything up. Math is changing because of proofs like theirs: Computer jocks like Stephen Wolfram insist that math needs to get beyond its infatuation with axioms, while string theorists say their results just can't wait for rigorous proof. And strangely, mathematicians are even starting to teach machines to prove theorems on their own. So maybe some day computers will explain why four colors are enough, in terms we can understand.


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2014 Electonics Engineering Board Examination passer 2014 Electronics Technician Board Examination passer Trigonometry, Math, Intermediate Algebra, Differential Equations, Calculus 1, Calculus 2 Project Engineer at Smart Communications, Inc . 2014 Electonics...
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From September 2015 the course covers the new 6 areas of Mathematics using the new 9-1 grading system:
- Ratio, proportion and rates of change
- Geometry and Measures
Building on the work completed at Key Stage 3.
There are still two tiers of entry for Mathematics. The Higher tier covers grades 4 to 9 and The Foundation tier covers grades 1 to 5. A student’s Maths set will determine which tier of entry they take. Each tier covers all areas of Mathematics. Students are set across the whole year group based on their ability and their results during Key Stage 3.
There is no coursework for Mathematics as everything is exam based.


MATHS Week -October ‘22
Our friends in 5th & 6th class were working with us on “Telling the Time, Fun with Number & Problem Solving”.
They taught us a lot and we got to know them better too. It was great to be able to chat with our tutors about math problems and how to solve them. We learned that there are lots of different ways to solve a problem.
The Case of the MISSING Pencil Case!
With Help from our Tutors.
6th Class helping First Class to learn how to tell the time.
Who knew using a Dice could be so much fun during Maths


You’ve never considered yourself much of a math whiz. You passed grade-school level math classes just fine, but not easily. Today, you work in a job that doesn’t require heavy use of mathematics.
That said, you’ve recently decided to take up woodworking, which several friends have told you involves math. Does woodworking involve math?
Yes, woodworking is quite mathematical. You must not only know basic math such as decimals and fractions but more advanced concepts such as geometric shapes and angles as well. Otherwise, your woodworking projects won’t be accurate.
Although many people think math isn’t fun, harnessing the power of mathematics will make you a far better and more talented woodworker.
Ahead, we’ll elaborate on which math concepts you should learn. Think of this as your math 101 class. Further down in this article, A link to a youtube video that will be very useful to you.
Let’s get started!
What Kind of Math Do You Need to Know to Be a Good Woodworker?
In woodworking, you will create many projects of all shapes and sizes. Without understanding geometric shapes, it’s hard to visualize what your project will look like and get it to the exact dimensions you want.
Let’s talk about geometric shapes a bit. A geometric shape is defined as any area or figure that has lines, points, and/or curves that allow the boundary to close. The most common geometric shapes are squares, rectangles, circles, and triangles.
A square is considered a regular quadrilateral in geometric terms. Its angles, of which there are four, are all equal. Its sides are equal as well. Squares have four sides and internal angles of 90 degrees.
Rectangles are like longer squares, but geometrically, they’re known as quadrilaterals. Each of their four corners is a right angle, making a rectangle an equiangular quadrilateral as well. This is just another way of saying that each corner is 90 degrees.
A circle has rounded, curvy sides rather than straight, pointy ones like a square or rectangle. Each point on its plane is at the same distance from the circle’s center point.
Triangles have three vertices and edges. Different types of triangles exist, such as:
- Isosceles triangle: If two sides of the triangle are the same length, then it’s an Isosceles triangle.
- Acute triangle: A longer and leaner triangle, an acute triangle has angles that add up to 180 degrees. Two angles are acute and the third is obtuse.
- Right triangle: The right triangle features one right angle of 90 degrees, typically in the corner. The other side is considered the hypotenuse.
- Equilateral triangle: As the name suggests, equilateral triangles have equal angles on all three sides. These are typically 60-degree angles.
- Equiangular triangle: All vertex angles are the same with an equiangular triangle.
Geometric shapes also include parallelograms and polygons. A parallelogram has two opposite sides that are parallel to one another. Polygons are non-curved shapes with lines and mostly closed parts.
Examples of polygons are decagons (with 10 sides), nonagons (with 9 sides), octagons (with 8 sides), heptagons (with 7 sides), hexagons (with 6 sides), pentagons (with 5 sides), quadrilaterals, and triangles.
Many geometric shapes feature angles, but angles are also worth discussing on their own. Getting the precise angle correct when building a woodworking project like a shelf or a bookcase is absolutely necessary, so make sure you study up.
What is an angle? When two sides or rays meet at a vertex or endpoint of a figure, these are angles. Outside of plane geometry, angles are sometimes defined as a measure of rotation as related to a length ratio to the circular arc of a radius.
If you thought you were done with terms like obtuse and acute after learning geometric shapes, these terms come back to describe the types of angles as well. Here’s what you need to know.
- Full rotation: A full rotation angle is 360 degrees, hence the rotation this angle is named after.
- Reflex angle: Any angle that surpasses 180 degrees is known as a reflex angle.
- Straight angle: When an angle measures exactly 180 degrees, it’s a straight angle.
- Obtuse angle: An obtuse angle is between 90 and 180 degrees. This angle exceeds 90 degrees but doesn’t quite reach 180 degrees.
- Right angle: As we talked about with triangles, a right angle is precisely 90 degrees.
- Acute angle: Any angle that’s less than 90 degrees is an acute angle.
Knowing which angle is which will make cutting your wood far simpler. For example, if you wanted to divide a right angle (or one that’s 90 degrees) when woodworking, you could use a straightedge to make a line down the middle of the corner. Then, with a miter saw, split the corner to get two 45-degree angles.
Did you pay attention in algebra class? If so, then you may remember decimals. If that lesson is foggy by now, then here’s your recap. A decimal is a number with a fractional part and a whole number part punctuated by a period or a decimal point. Any number after the decimal has a value that’s less than 1.
Let’s take a random number with a decimal, 45.6. In this instance, the 4 represents the tens, the 5 represents the ones, and the 6 is tenths. You always want your decimal between the ones and tenths.
In woodworking, when you make measurements for your project, you might sometimes find your calculation returns a decimal point. Understanding what each number before and after that decimal point means will keep your measurements exact so your project comes out right.
In some scenarios, you might even opt to round up the decimal point. If you’re going to do that, then your number must have at least two digits after the decimal point. For example, instead of 45.6, let’s say your number was 45.61 instead.
Any digit after the tenths that is under 5 in value means you do not round up the tenths number. So 45.61 would still round out to 45.6.
If your number was now 45.67, since 7 is greater than 5, you’d round up to 45.7. The same is true if your number was 45.68.
In determining the number to round up to, you always take the number in the tenths spot and add 1.
Besides decimals, you could also stumble across fractions when following woodworking tutorials online or even coming up with your own recipes. Fractions are a little more difficult to understand than decimals, but not impossible by far.
To grasp how fractions work, think about a pizza pie. It’s sliced into 8 pieces, all of equal size. When your fraction reads something like 3/8, that’s three-eighths of the pizza pie.
What does this mean? The top number, or the 3, is how many slices remain. The bottom number, or 8, tells you how many slices the pizza is cut into.
One-quarter or ¼ means there are 4 slices of pizza and 1 slice remains. This slice is going to be bigger than when comparing a fraction like 3/8ths because there were only ever 4 slices instead of 8, but you’re still comparing a circle of the same size.
One-half or ½ is only 2 slices of pizza, with a single slice remaining. Think of it like this: if you ordered a pizza and, with your pizza cutter, split the whole thing down the middle and said that’s 2 pieces, that’s what ½ looks like visually.
Resources for Learning Math in Woodworking
The above descriptions of mathematical concepts involved in woodworking should be a good starting point for you. If at any point, you find you need more detailed instruction, we gathered up a few resources you can rely on.
With Begnal’s guidance, the Popular Woodworking book is supposed to teach you how to set your woodworking machine to the correct speed, how to take a piece of furniture and transfer its dimensions to a drawing, and how to determine the quantities of wood needed for all sorts of projects.
You can get the book on Amazon as a spiral-bound or hardcover.
Math in Woodworking Series On YouTube
RRR Woodworks is a YouTube channel that hosted the Math in Woodworking series. Across four episodes, you can learn all sorts of handy woodworking concepts. The first episode centers around using dados to calculate dimensions.
In the second episode, RRR Woodworks covers using decimals and fractions for precision wood-cutting. The third episode discusses trigonometry and how it can help you determine the right angle for cutting wood. The fourth and last episode is about tree height for if you ever cut down a tree to obtain your own wood.
While there are only four episodes, each is about 10 minutes and rife with information you’ll surely use. Plus, YouTube is a free instructional resource, which makes it great to learn from.
The third resource we recommend for new woodworkers learning math is the website Carpentry Math. You can refresh your memory on geometric shapes, angles, and more on this site, using formulas to do your own calculations.
The cool thing about Carpentry Math is how they also offer calculators as well as plans for woodworking projects. These include bird feeders, birdhouses, benches, picnic tables, and even a deck or set of stairs. It’ll soon be time to get building!
If you weren’t great at math in school, it’s never too late to learn. You will need to know math concepts involving geometry, algebra, and trigonometry to excel at woodworking. With the information and resources in this article, you’re well on your way to becoming a math master and thus a better woodworker. Good luck!


Located here are the COMMON CORE Standards for English Language Arts and Mathematics.
For more information, please visit: www.corestandards.org/the-standards.
Here are some links for Mathematical Practice Resources:
bestcase.wordpress.com/2011/07/22/mathematical-practices/ (rubrics for mathematical practices)
(mathematical practices posters, screen beans, individual posters, practices at a glance, and cubes for students to roll to embed mathematical practices)
departments.jordandistrict.org/curriculum/mathematics/elementary/CCSSM6/SMPposters.pdf (posters used in this powerpoint to convey the mathematical practices)
**Go under RESOURCES at the top of the homepage to choose a specific grade level **Within each g/level are each of the standards **EACH standard can then be clicked on where you're taken to another page that can include some or all of the following:
>Videos of teaching/lessons
>Interactive computer games/activities for that standard Direct links to
>IXL activities for practice on the standard
At the bottom of the grade level links there is are links for high school math as well as a link specifically for the Mathematical Practices.


If you’re involved in the logging industry, you know that calculating the volume of logs is a crucial task. Log volume calculation is necessary for determining the amount of timber harvested, the revenue generated, and the transportation logistics.
In this article, we’ll take a look at log volume calculators, how they work, and the different types available. We’ll also discuss the advantages and limitations of each method.
What is a Log Volume Calculator?
A log volume calculator is a tool used to estimate the volume of a log based on its dimensions. It is designed to provide an accurate measurement of the log’s volume, which is crucial in determining its value.
The calculator uses various mathematical formulas and algorithms to compute the volume of logs in different shapes, including cylinders, cones, and irregular shapes.
How Our Log Volume Calculator Works
Our log volume calculator is based on a simple and easy-to-use interface. To use the calculator, simply input the length, diameter, and shape of your logs, and the calculator will provide an accurate estimate of the volume of your logs. The calculator takes into account the specific shape of each log, including the taper and curvature, to provide a more accurate estimate.
See Also: Screw Length Calculator.
Benefits of Using Our Log Volume Calculator
- Accurate volume estimates: Our log volume calculator provides accurate and reliable estimates of the volume of logs, ensuring that loggers can make informed decisions about their operations.
- Time-saving: By using our log volume calculator, loggers can save time compared to manual log volume calculations. The calculator can provide volume estimates for multiple logs in a matter of seconds.
- Cost-effective: Using our log volume calculator is a cost-effective solution for loggers, as it eliminates the need for expensive manual measurements and calculations.
- Easy to use: Our log volume calculator is based on a user-friendly interface, making it easy for loggers to use, even if they have no prior experience with log volume calculations.
How to Use Our Log Volume Calculator
Using our log volume calculator is simple and straightforward. Follow these steps to get started:
- Input the length of your logs in meters
- Input the diameter of your logs in centimeters
- Select the shape of your logs (e.g. round, rectangular, etc.)
- Click the “Calculate” button to receive your volume estimate
Log Volume Calculator
The Importance of Accurate Log Volume Calculations
Accurate log volume calculations are crucial for optimizing a logging operation. Loggers rely on these calculations to determine the cost and efficiency of their operations, and to ensure that they are selling their logs at the highest possible price. Inaccurate log volume calculations can result in loggers selling their logs for less than they are worth, or spending more on transportation and processing than necessary.
See Also: Plywood Calculator Cut List.
How do you find the volume of a log?
To find the volume of a log, you can use the formula for the volume of a cylinder.
How do you measure a log in cubic meters?
The amount of wood in a log can be measured in cubic meters by calculating its volume.
How do you determine the amount of wood in logs?
The amount of wood in logs can be determined by measuring their diameter, length, and taper.
How is the amount of wood measured?
The amount of wood is measured by its volume or weight.
What does the term “log volume” mean?
Log volume refers to the amount of wood contained in a log.
What is the purpose of calculating log volume?
Calculating log volume is important for estimating the amount of wood that can be harvested and sold.
How do you apply the formula for log calculations?
To use the log formula, you need to know the base and exponent of the logarithm.
What is meant by the term “logarithmic calculation”?
Logarithmic calculation involves using logarithms to solve mathematical problems.
our log volume calculator is a valuable tool for loggers looking to maximize their profits and optimize their operations. With its accurate and reliable volume estimates, time-saving capabilities, cost-effectiveness, and easy-to-use interface, our log volume calculator is the ideal solution for loggers looking to streamline their log volume calculations.
Try our log volume calculator today and start maximizing your log volume.


Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe. To be sure, they do not point to the personal God of the Bible as such. Yet they are not inimical to the biblical God, either. The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God.Since my last exposure to high math was a Calculus class I dropped in the second semester of my freshman year at college (and that was a long time ago), I emailed the article to a mathematician friend of mine to see if it held water. He wrote back with an affirmative, also recalling the time he personally stumbled across one on his own: “if you are creating a code like a newspaper cryptogram that involves matching each letter with a different letter, and you do it randomly, the probability that a random matching does not match any letter to itself rapidly approaches the number 1/e. There is a God and there is order in the universe is my reaction to something like that.”
I don't much understand that, but I get the point. He signed off with a quote by the mathematical genius Erdos who just died a couple years ago: “God has a big book with all the best proofs of all the best theorems in it. If you are fortunate, he might open the book just a bit and let you see one of those proofs. And you don't even have to believe in God; but you must believe in the book."
The proof then, as they say, is in the numbers.
(Image: jam343 - and no, I have no idea what it means, but I do know big words like "elucidation")


Introducción a la Filosofía Matemática
Próximamente en Coursera. Más info, aquí.
Introduction to Mathematical Philosophy
Hannes Leitgeb and Stephan Hartmann
|July 2013 (8 weeks long)||Sign Up|
About the Course
As we will try to show, one can analyze philosophical concepts much more clearly in mathematical terms, one can derive philosophical conclusions from philosophical assumptions by mathematical proof, and one can build mathematical models in which we can study philosophical problems.
So, as Leibniz would have said: even in philosophy, calculemus. Let's calculate.
Week Two: Truth.
Week Three: Rational belief.
Week Four: If-then.
Week Five: Confirmation.
Week Six: Decision.
Week Seven: Voting.
Week Eight: Quantum Logic.


The concept of dimension and shape fractal geometry
Fractal geometry a fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale if the replication is exactly the same at every scale, it is called a self-similar pattern. Analytic and numerical calculations of fractal dimensions arman shamsgovara [email protected] under the direction of gaultier lambert. Request pdf on researchgate | fractal methods and results in cellular morphology - dimensions, lacunarity and multifractals | this paper discusses the concepts of fractal geometry in a cellular biological context it defines the concept of the fractal dimension d, as a measure of complexity and illustrates the two different general. Fractal geometry almost all geometric forms used for building man made objects belong to euclidean geometry, they are comprised of lines, planes, rectangular volumes, arcs, cylinders, spheres, etc these elements can be classified as belonging to an integer dimension, either 1, 2, or 3 this concept of dimension can be described both.
The koch snowflake (also known as the koch curve, koch star, or koch island) is a mathematical curve and one of the earliest fractal curves to have been described it is based on the koch curve, which appeared in a 1904 paper titled on a continuous curve without tangents, constructible from elementary geometry (original french title: sur. This paper has applied the concept of fractal geometry in designing a grid-shell-like complex spatial structure the property of the fractal dimension which characterizes the level of roughness of a shape has been particularly explored in this study for designing a complex-shaped spatial structure by taking a paraboloid as a basic shape of reference. Question sent by jose galán (alacant) eduardo ros answers: «clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel a straight line» are benoît mandelbrot’s genius opening lines for his book the fractal geometry of naturemandelbrot enunciated the concept of fractal.
Concept of fractals introduced by mandelbrot , which has the shape formed in nature, has been usually analyzed using euclidian geometry the key parameter for fractal the key parameter for fractal. In mathematics , more specifically in fractal geometry , a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured it has also been characterized as a measure of the space-filling capacity. In fractal geometry, on the other hand, dimension is treated as a continuum a a curve’s dimension, for example, can take on any non-integer value between 1 and 2.
A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension  and may fall between the integers  fractals are typically self-similar patterns, where self-similar means they are the same from near as from far [3. Any mathematical concept now well-known to school children has gone through decades, if not centuries of refinement a typical student will, at various points in her mathematical career -- however long or brief that may be -- encounter the concepts of dimension, complex numbers, and geometry if. The key concept in chaos theory is that an order is laid in any disorder this means that discipline should not be sought only in a scale chaos is a theory that considers various issues, but requires a language for its concepts visualization and this was an area that created geometry of chaos or fractals fractal geometry provides us a tool for. Fractal geometry math carla moreno 6th period the concept fractal geometry , also called the “true geometry of nature” could be explained as: non-triangular or squared shaped figures, but as more complex ones fractals are used to explain concrete objects slideshow 4940703. The concept of fractal dimension was defined for true fractal objects and is formally defined in ref 3 3 b b mandelbrot, the fractal geometry of nature b b mandelbrot, the fractal geometry of nature.
He stated that fractals (through fractal geometry) are more useful to describe natural shapes than the classic euclidian geometry describes financial volatility measurement using fractal dimension keywords: discontinuous functions interpolation approximation functional spaces fractals. The relationship between the fractal dimension and shape properties of particles the shape of particles is not accurately described by euclidian geometry however, fractal geometry uses the concept of fractal dimension, dr, as a way to describe the shape of particles in this study, the fractal dimensions and shape properties of particles were. The shape in the antenna that can have non-integer values, called a fractal dimension this means that, shapes in the antenna can have irregular shape than regular shape.
Dimension is at the heart of all fractal geometry, which provides a reasonable basis for an invariant between different fractal objects there are also experimental techniques. Geometry ( geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space geometry is one of the oldest sciences initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century bc geometry was put into an axiomatic form by euclid, whose treatment—geometry.
The fractal geometry of nature dimension and fractal dimension • the discovery of space-filling curves, such as the peano curve, had a major impact in the development of the concept of dimension: questioned the intuitive perception of curves as one-dimensional objects • points are zero-dimensional, lines and curves are one. 15 jagadeesha, ambresh, raj and madhusudhana ii design consideration fractal geometry with base shape of plus shaped with ebg. Is made by using concept of fractal geometry vertical length of 27 mm is divided into 3 parts, each of length 9 mm vertical length of 27 mm is divided into 3 parts, each of length 9 mm these two cuts are made in vertical direction to form h shape patch h shaped patch vs having five squares this h.


Tables 2 to 20 – Multiplication Tables
The mathematical topics which are taught in elementary school and the later also consider tables 2 to 20 as a base. The tables from 2 to 20 serve as a foundation for students to learn other mathematical skills. Multiplication tables 1 to 10 or 1 to 100 are used while performing other mathematical operations too. It is advisable to properly memorize these maths tables to make calculations easier in everyday life. Learning these tables can also be one of the ways to keep your kid engaged and away from the screen. You can play quiz and puzzles on the same with them rather then they watching some video for long.
1 to 10 Table
Students are advised not to rely on calculators to calculate basic maths. The basic tables like a table from 1 to 10 or 2 to 20 shall be on the tips of the student. These tables not only helps in solving maths in class but also in everyday life.
Table from 11 to 20
To learn the tables after10, i.e tables from 11 to 20, you are supposed to learn previous tables first. You should do it in such a way that you are able to recall the tables immediately you see the numbers to be multiplied.
Tables from 12 to 20
Now that you have learnt the tables from 1 to 11, you can start learning the rest of the tables from 12 to 20. To confirm whether you know the right table answers, you can take a quiz. If you realize you need more practice, you can always go back to the multiplication chart.
Tables from 13 to 20
If you master the tables from 13 to 20, you’ll surely be able to excel in all maths topics. It would be easier for you to do the calculations if you by heart these. In the same way, you can learn other tables too.
Tables from 15 to 20
Tables from 15 to 20 are the most crucial multiplication tables. When you learn these, you can also learn tables from 1 to 100 too. In short, Learning mathematical topics using the tables will always help in solving the sums easily and quick. There are many ways to teach maths tables to kids. whatever way you follow, just make sure you enjoy it and remember all the tables.


Marcus du Sautoy
From Verified Handles
British professor of mathematics
Marcus Peter Francis du Sautoy (; born 26 August 1965) is a British mathematician, Simonyi Professor for the Public Understanding of Science at the University of Oxford, Fellow of New College, Oxford and author of popular mathematics and popular science books. He was previously a fellow of All Souls College, Oxford, Wadham College, Oxford and served as president of the Mathematical Association, an Engineering and Physical Sciences Research Council (EPSRC) senior media fellow, and a Royal Society University Research Fellow. from Wikipedia
These are provided for reference and have been verified to be accurate.


Why don't fictional characters say "goodbye" when they hang up a phone? If we can't tunnel through the Earth, how do we know what's at its center? All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.
Hottest Questions. Previously Viewed. Unanswered Questions. Painting and Staining. Math and Arithmetic. How many square feet does a quart of paint cover? Wiki User One quart of most common paints will cover about 70 square feet.
A quart of paint covers square feet of primed wall surface. It might cover 50 square feet of unprimed surface if you're lucky, so always prime before painting. The coverage of paint depends on the texture of the surface that is being painted. Theoretically, a quart of ordinary house paint, spread at 4 mils thickness on a smooth surface will cover square feet.
However, as texture of the surface increases, the coverage will drop. A quart of paint could yield 50 square feet or less on a rough stucco or corrugated surface.
Asked in Area How many sq ft does one qt of paint cover? One quart of paint nominally covers about square feet. Asked in Painting and Staining How many gallons of paint will cover square feet? It will take approximately five to six gallons of paint to cover square feet. The general rule is to square feet out of a gallon of paint.
Asked in Area How much paint is needed to cover square feet? It is estimated that a gallon of paint can cover about square feet of wall space. So if you only need to cover an estimated one hundred square feet then one gallon of paint should suffice. One gallon of average house paint will cover about square feet.
About square feet. Between 1, and 1, square feet. Asked in Cooking Measurements, Volume How many feet can you paint with a gallon? An average gallon of latex house paint will cover square feet. If your drum is a 55 gallon drum and your paint can cover square feet per gallon then you may cover one coat only a square almost by feet.In this article, we offer insight to answer the conundrum of how much stain you should buy to complete a project.
If you have questions on how to estimate the number of supplies to purchase for a project, feel free to leave us a comment with pictures. Once this calculation is considered, you can figure out how many gallons of deck stain you need by reading the coverage rate of the stain you are buying.
On average most deck stains cover sq. When measuring your deck it is best to use a tape measure or measuring wheel. If you do not have access to a measuring device you can come up with a close approximation by stepping the deck off. For example, to measure the floor stand on one end and with long strides walk to the opposite end counting each step.
A long step is close to a yard, which equals 3 feet. Multiply the number of steps you took by 3 and that is the total number of feet. Once you have a total square footage number you will then know how much deck stain you should buy to complete the project. Always buy a little extra if you can just so you do not run short. You can return any unopened cans to the store or just save them for next time the deck needs to be refinished.
Just had sq. Deck installed with rails and 3 sets of steps. After I stain my new treated pine deck will it take the same amount of stain for the second coat or less.
How do I figure how much for the second coat? All clear sealers will not provide UV protection from graying. I do not understand your question. Coverage also varies on the stain brand and type you are using. I am re-staining a deck that was done about 4 years ago. It has held up pretty well but will need a good cleaning and light sanding in spots. It is unclear whether on-line calculators used to estimate how much stain to buy assume that the deck has never been stained before or that the deck was stained previously.
The deck is about sq ft. I have rails, spindles, steps, soffits and lattice. Their measurement was sqft while mine was sqft. As a contractor myself I never give an estimate in which the number doesnt end in either zero or 5. If a contractor gave you a number like yours, then they usually will end up needing more. Always round up. Here is why, you have waste in materials. You also have the fact that we havent been able to test to see how your wood will soak up the product. Many factors.
Also, 32 square feet isnt a huge number. If he was or square foot off then you would second guess it. We bought a house with a deck of square feet. The wood is very porous since it should have been done quite awhile ago. How much should we buy?By Gene Hamilton, Katie Hamilton. Estimates require specific calculations for each surface you want to paint. To estimate the amount of paint you need in order to cover the walls of a room, add together the length of all the walls and then multiply the number by the height of the room, from floor to ceiling.
Is that math class coming back to you now? Now you have to determine how much of that square footage is paintable surface area.How Much Deck Stain do I Need? - Thompson's WaterSeal
Because you use a different paint on the doors and windows, subtract those areas from the room total. No sweat, just subtract 20 square feet for each door and 15 square feet for each average-sized window in the room.
You end up with a number that is close to the actual wall area you have to cover with paint. In general, you can expect 1 gallon of paint to cover about square feet. You need slightly more than a gallon if the walls are unpainted drywall, which absorbs more of the paint. You also need to consider whether to paint more than one coat. When painting a dark color, pros often add a color tint to the white primer.
Tints for both latex or alkyd paints are available at most paint stores. Now for the clincher of the math problem. Divide the paintable wall area by the square-foot coverage in each gallon can to find the number of gallons of paint you need for the walls. You can round uneven numbers; if the remainder is less than. Of course, buying in bulk is usually more economical, so you may discover that 3 quarts of paint cost as much as a gallon. Use the following formula to estimate the amount of ceiling paint you need.
Double the result if the ceiling requires two coats. Divide that number by the estimated square feet covered per gallon to figure out how many gallons of paint you need. Use the following formula to estimate the amount of wall paint you need. Double the result if the walls require two coats. Divide this figure by the paint coverage square feet per gallonand the result is the number of gallons to purchase.
For this example, you want to buy 1 gallon and 2 quarts of paint for a single coat. Include all the trim around doors and windows, at baseboards, along the ceiling, and for any built-in furniture. As an example, imagine that you have ceiling molding running around a room that is 14 feet wide and 20 feet long. Determine the total length of molding around the room by adding together the length of all the walls that the molding covers. Divide this number by to estimate the gallons of paint required to cover the molding.Onan marquis gold 5500 carburetor
The result in this example is much less than a quart, but you may paint other woodwork in the room the same color, so buying a full quart may not be terribly wasteful. Multiply the number of doors by 20, doubling the answer if you plan to paint both sides.By Crowder Painting. Using two cans mixed at different times can result in obvious color differences. Many formulas recommend measuring each wall separately, determining their square footage, and then adding all the measurements together.
This idea works great for interior walls but not so well for exterior surfaces where the roughness or porosity will increase the amount of paint or stain needed. Each side of your home needs a separate measurement and total square footage.
Measure the length then the highest point in feet. Multiply these together for a total square footage, repeat for each side. This will give you a good accurate square foot total for estimating exterior paint, primer or stain. How much surface area a paint or stain will cover depends on many variables. Unprimed and heavily textured or porous surfaces will require more paint than a smooth, primed one.
The first coat usually requires more paint than subsequent coats. Additionally, different types of paint and stain are formulated for different purposes-therefore, they cover differently.1957 ford fairlane interior kits
For estimating paint or stain, however, here are some good guidelines:. For any smooth surface the square footage is increased. Many rough surfaces will require either multiple coats or thicker coats to achieve a finished look. Another consideration is application method.
Always pour the product into a paint tray or another container, instead of working directly out of the can. And, store leftover paint and stain in the smallest possible container to prevent hardening. Paint stores carry empty paint buckets that are perfect for this. Label cans with a dab of the paint inside them to make it easy to find the right color when you need it. Seal paint and stain cans carefully and always keep them well out of reach of children. Your email is never published nor shared.
All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.
Painting and Staining.
How many square feet does one gallon of stain cover? Wiki User Depending on the placement and thickness of the shakes, anywhere from to square feet per gallon. Asked in Painting and Staining, Math and Arithmetic, Area How many square feet does a gallon of semi-transparent stain cover? It depends on the surface it's going on, but generally between square feet. Asked in Area How much paint is needed to cover square feet?
It is estimated that a gallon of paint can cover about square feet of wall space. So if you only need to cover an estimated one hundred square feet then one gallon of paint should suffice. One gallon should cover at least square feet for smooth surface, for rough.
Asked in Cooking Measurements, Volume How many feet can you paint with a gallon? An average gallon of latex house paint will cover square feet. If your drum is a 55 gallon drum and your paint can cover square feet per gallon then you may cover one coat only a square almost by feet. He covered square feet per gallon. One gallon of average house paint will cover about square feet.
Asked in Painting and Staining, Math and Arithmetic, Area What is the formula to calculate how many square feet a gallon of paint will cover?
A gallon of paint one coat will cover about square feet; if surface is very smooth about sq ft,and if very rough maybe sq feet. Asked in Painting and Staining How many gallons of paint will cover square feet? It will take approximately five to six gallons of paint to cover square feet. The general rule is to square feet out of a gallon of paint. Asked in Paint Jobs How much would one gallon of primer cover? For many paints, one gallon will cover square feet.
Estimating How Much Paint to Buy
However, the quality of the paint can affect how much it will cover. Asked in Painting and Staining, Math and Arithmetic, Area, Decorating One gallon of latex paint will cover approximately how many square feet?
However, this will depend on how rough the surface is and how different the current area to be covered is. If it's a smooth surface and you're painting a similar color, 1 gallon should cover sq.Stain can change the look of your fence to match your home or landscaping without covering up the beautiful natural grain of the wood. Estimating the amount of stain you'll need saves time and money by letting you purchase all the stain you'll need in one trip without buying more than you'll actually need.
Measure the length and height of the fence to be stained.
How Much Paint Do I Need? - Home Decorating & Painting Advice
Multiply the length by the height to determine the total square footage of the fence. If you are going to stain both sides, multiply the square footage by two. Note the coverage provided by the stain you plan to use. This is usually listed on the side of the can. Different stains offer different coverage, although it is often between and square feet per gallon. Divide the total square feet of fence to be stained by the coverage listed on the can. For example, if you have 1, square feet of fence and the stain says that 1 gallon covers square feet, you would divide 1, bywhich equals 5 gallons to cover the fence.
Fiberglass Supply - Carbon Fiber and Composite Supplies for the 21st Century
If you get a fraction in your answer, always round up to the next whole gallon. Skip to main content. Customer Service Newsroom Contacts.Calculating how much stain to use on a floor is not a difficult task, but some measuring and basic math skills are required.
The square footage covered is listed on the stain container as a guide, as well. However, you also must factor in how porous your wood floor is, how you will apply the stain, and whether you will apply one coat or more. Once you have all the information, you are ready to purchase stain. Measure the length and width of the floor. If the floor is not rectangular or square, measure as close as you can to a rectangular or square shape.
Measure the length and width of additional areas you wish to stain, such as doorways, closets or hallways. Multiply the length by the width of the larger area to determine the square footage of the area.Coinmama login
Multiply the length by the width of the hallway, closet or doorway areas to determine their square footage. Add the square footage of the hallway, closet and doorway areas to that of the main area.
Check the square-foot coverage on the can of stain you have chosen. Divide the total square footage of the area you want to stain by the square footage covered by a can of your chosen stain.
Round the result up to the next whole number. For example, if you have square feet of floor to cover and a can of stain covers square feet, you need two cans of that stain. However, this is only an approximation of the number of cans of stain you will need before factoring in the type of wood and the application process. Determine what kind of wood is on your floor. Oak is a popular wood for floors, but it is porous and will soak up more stain.
Ash and chestnut are similar to oak. Pine, cedar or fir only needs a light application of stain. Maple is a dense wood that does not absorb stain easily, so it may need two coats. Decide how you will apply the stain. If you spray on the stain, less is used. If you use a brush, allowing you to work the stain into the wood, more stain is used.
Decide whether you will apply one or two coats of stain. If you want a darker effect or if the wood is dense, you may want to apply two coats. Therefore, you will need to double the amount of stain you purchase. Consider the calculated number of containers, type of wood and application. If the wood is porous, and you are using a brush, buy an additional container of stain.
If the wood is pine, cedar or fir, you may not need more than the calculated number of cans of stain. Pauline Gill is a retired teacher with more than 25 years of experience teaching English to high school students.
She holds a bachelor's degree in language arts and a Master of Education degree. Gill is also an award-winning fiction author. Skip to main content. Tips Wipe off excess stain soon after you apply it to avoid uneven color. Oil stains allow you more working time. Water stains dry faster, but have less odor. Save money by purchasing stain in gallon containers instead of quarts if you determine you need a large amount of stain.
Warnings Do not stain your floor in an enclosed room.Uni fiis directorio
Make sure the room is well ventilated.
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If you and your kids are playing on the ground, you can use these kinds of dice while playing. There are some mathematical games in which you can use these dice. I found this online them as I usually play in the yard with some of my friends. I play some kind of mathematical games, so these dices help me a lot. I am sharing some pictures of these dice with you, have a look at these pictures.
If you bought this superb polished table in a store, it would cost you a fortune, but our detailed instructions will help you make one for less than $100. And it looks like highly polished stone, but no-one would know it’s actually made from concrete with a wooden base. Also, you can embellish the top with leaf prints, like the table shown here, or personalize it with glass or mosaic tiles or imprints of seashells.