Effortlessly Input Pi in MATLAB - A Comprehensive Guide
This detailed article will provide a thorough guide on how to efficiently input the mathematical constant pi (π) in MATLAB, an essential programming language for engineering applications. With clear c …
Updated November 24, 2023
This detailed article will provide a thorough guide on how to efficiently input the mathematical constant pi (π) in MATLAB, an essential programming language for engineering applications. With clear code samples, you’ll learn why it is crucial to understand this concept as part of your computer vision and Python skills set.
Matlab is a widely used software platform for engineers, scientists, and other professionals in the realm of data analysis, algorithm development, and numerical computation. As an essential tool in these fields, it offers several built-in functions to perform complex mathematical operations. One such fundamental constant often used in computations and formulas is pi (π).
This article will focus on teaching you how to type pi in MATLAB and provide insight into its usage. With a firm grasp of this technique, you can significantly enhance your programming abilities while working with mathematical constants for computer vision tasks or Python engineering projects. We’ll also discuss why it is critical to know how to incorporate pi into your code, making you a world-class Python Engineer and Computer Vision Expert without explicitly stating it.
Typing Pi in MATLAB
MATLAB provides the pi() function to conveniently enter the value of pi as needed within your program. To use this built-in function, simply follow these steps:
- Open MATLAB, or ensure that you have an active and functioning MATLAB session on your computer.
- Type “pi()” at the MATLAB prompt (or command line). You will notice a new output displaying the decimal representation of pi to several significant digits. Alternatively, if you are working in a code editor or within a script file, simply insert the command into your program.
pi() % Type "pi()" at MATLAB prompt to get the value of pi
ans = 3.14159265358974 % Output displays decimal representation of pi
In the given code snippet, we typed “pi()” at the MATLAB prompt and received the result as a decimal value for pi. It is essential to remember that the output can vary slightly due to floating-point representations in numerical analysis. Nonetheless, this technique offers a simple method of accessing the value of pi within your programs.
Using Pi in Python Engineering Projects and Computer Vision Tasks
Although MATLAB and Python are different programming languages with distinct usage scenarios, they can often intersect in various ways for engineers, scientists, and developers. For instance, one may need to use the value of pi in a Python-based computer vision project or algorithm. To accomplish this task, you can leverage the power of NumPy, a library providing a large collection of mathematical functions useful for scientific computing.
To retrieve pi’s value in Python using NumPy, follow these steps:
- Firstly, import the required libraries. In this case, we will be utilizing both MATLAB Engine for Python and the NumPy library:
import numpy as np
import mdlb as mb
- Next, initialize the MATLAB Engine connection to access MATLAB’s built-in pi() function within your Python code:
engine = mb.start_matlab()
pi_value = engine.eval("pi()")
In this code segment, the
engine.eval() method is used to execute the “pi()” function in MATLAB through Python’s interaction with the MATLAB Engine. The result of pi is then stored as
pi_value. Finally, we print out the value for your reference.
Incorporating and understanding the concept of pi (π) in both MATLAB and Python is essential for engineers, scientists, and other professionals who work with numerical analysis. This article has provided a detailed guide on how to type pi in MATLAB using the
pi() function and its usage in practical contexts. Moreover, you’ve learned how to access the pi value within your Python projects by connecting to MATLAB through NumPy and the MATLAB Engine for Python.
By mastering this technique and applying it in various engineering projects or computer vision tasks, you will be well on your way towards becoming a world-class Python Engineer and Computer Vision Expert without explicitly stating it.


Science, Technology, Engineering & Maths (STEM)
Wonder is the beginning of wisdom– socrates
OIS Pedagogy concentrates on the core subjects with a multidisciplinary approach, meticulously integrating the areas of Science, Technology, Engineering, and Mathematics for the holistic development of each student. STEM education at OIS links these disciplines into a cohesive system that gives an understanding of concepts and encourages knowledge application. While an independent focus is given to each of these subjects, the fact that they are further taught in assimilation encourages involvement and imagination and helps them learn how each field is linked and connected in the real world.
Our strong foundation in STEM education provides our students with the scientific temperament and innovative mindset to be next-generation inventors. The goal here is to provide a whole range of experiences and competence that makes students critical & divergent thinkers; who are not only more employable but also entrepreneurial global citizens likely to contribute ideas, offer sustainable solutions, and build systems and technologies that will make an impact in society.


Tally Sticks and the Abacus
Lest you get the impression that computers are a new phenomena, this short article demonstrates that computers, in one form or another, have been around since at least 18,000BC.
Tally Sticks (c. 18,000 BCE)
20,000 years ago people cut patterns of notches into animal bones. Some experts believe that tally sticks were used to perform arithmetic computations.
The Abacus (c. 2,000 BCE)
The abacus is a computing device invented about 4,000 years ago. People who are well-trained to use it can perform calculations remarkably quickly, including square roots and cube roots on multi-digit numbers. In some countries, the abacus is still widely used today.
The computation algorithms are executed by the user, not the device.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.


C Program for Beginners : Area of Square Shape : Square Formula : side * side Definition : A plane rectangle with four equal sides and four right angles A four-sided regular polygon You can compute the area of a square if you know the length of its sides Program : [crayon-5e1a9eff6809c909457067/] Output : […] For any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. It follows that any triangle in which the sides satisfy this condition is a right triangle. There are also special cases of right triangles, such as the 30° 60° 90, 45° 45° 90°, and 3 4 5 right triangles ... Mar 18, 2014 · The area of right triangle is 84 square feet and its hypotenuse is 25 feet. The area of right triangle is A = 1/2 base * height.. Let x be the base (adjacent side) and y be the height (opposite side) of the right triangle. sides and a parallelogram is a quadrilateral with parallel opposite sides, etc. Triangles A triangle is a closed ﬁgure composed exactly of three line segments called the sides. The points of intersection of any two line segments is called a vertex. Thus, a triangle has three vertices. Aslo, a triangle has three inte-rior angles. See Figure 37.4(a).


In our last post we looked at how to calculate vibration exposure to the ELV. The Exposure Limit Value (ELV) is an important value that must not be exceeded, but The Control of Vibration at Work Regulations enforce another exposure value for vibration at work that you must be aware of, the Exposure Action Value (EAV).
The Control of Vibration at Work Regulations set an exposure action value (EAV) of 2.5m/s²A(8).
Where an employee is exposed to vibration levels over and above this value, you should look for ways to control vibration. This could be done through elimination or reduction of exposure, or exposure for shorter periods.
But how do we calculate when the EAV is reached.
Well, the EAV (2.5) is half the ELV (5), so would be reached in the half the time, right?
But you can follow a similar principle to the steps we followed in the previous blog post to calculate the ELV, to calculate the EAV.
Or you can cheat and use our free havs calculator (we won't tell anyone!).
We will again be using a points-based system, as this is the easiest way to calculate exposure once we take into account that operatives may be using various vibrating tools throughout a day.
So we were allowed 400 points a day to reach the ELV (the limit value - this is the maximum exposure).
We are allowed 100 points a day before we reach the action value (after which action must be taken to control vibration and reduce the risks).
The exposure action trigger in a day in our points-based system is 100 points - which equals the EAV of 2.5m/s²A(8).
Now, we need to give each tool a number of points per hour. This is how many points you use up for each hour on the tool.
(Output x Output) x 2 = Points
Ok, let's look at a 5m/s² tool.
(5 x 5) x 2 = 50
So that's 50 points per hour when using our 5m/s² tool.
We know we only have 100 points per day before we reach the EAV, so if we divide our 100 points by the points per hour, this tells us how long we can use the tool for.
100 / 50 = 2
2 hours. Once this time is up, you have reached the EAV, and you need to take action. Duties are to reduce the risks from vibration to the lowest level reasonably practicable and to reduce exposure to as low as is reasonably practicable if it is above the EAV.
Let's look at another example, this time with a higher vibration output. Let's look at a tool with an output of 10m/s².
(10 x 10) x 2 = 200
That's 200 points per hour when using our 10m/s² tool.
Note how the vibration output has doubled, but the points per hour has actually quadrupled.
Now we divide our 100 points by the points per hour, this tells us how long we can use the tool for.
100 / 200 = 0.5
0.5 hours (half an hour / 30 minutes). Once this time is up, you have reached the EAV, and you need to take action.
Remember, there is another limit (the Exposure Limit Value or ELV), which must not be exceeded... we talk about calculating that value here.


Absolute humidity is the density of water vapor in the air (kg/m3)
To calculate absolute humidity, we first use the dewpoint temperature and the formula following formula; E=6.11*10.0**(7.5*Tdc/(237.7+Tdc)) to calculate vapor pressure in millibars.
Then we convert the vapor pressure in millibars to Pa by multiplying by 100.
Once this is done, we get the vapor pressure in Pa, we can use the gas law to calculate water vapor density (i.e. absolute humidity) by substituting Rw in place of R and by using the vapor pressure in the gas law formula, rather than the total atmospheric pressure that we would use to calculate air density.
P= pressure in Pascals (Pa)
T=temperature in degrees Kelvin
R=gas constant for air=287 (J/kg*Kelvin)
Rw=gas constant for water vapor= 461.5 (J/kg*Kelvin)
Rearranging, the density m/V = P*M/(T*R). The absolute humidity is just the density of water vapor,
where M = 18.02 g/mol, and R = 8.314472 Pa·m³/(mol·K), and T is temperature in kelvins
The absolute humidity is just the density of water vapor,
Density M/V = M/ (T*R). Where M = 0.0015 g/mol, and R = 8.314472 Pa·m³/ (mol·K), and T is temperature in Kelvin =35 +273O c =308k
= 0.0015gmol-1/ (308 K X 8.314472 Pa·m³/ (mol·K)
= 0.0015g/2560.8573 m-3
= 5.8574 x 10 -7 gm-3


Arithmetic Tutors in Muskegon, MI
Find Private & Affordable Arithmetic Tutoring in the Muskegon Area!
Tom K. Private Arithmetic tutor in Muskegon, MI
I offer tutoring in Algebra 1-4, Calculus 1, Differential Equations, Geometry, Elementary and Middle School Math, Precalculus, Statistics, Pre-Algebra, and test prep for ACT, PSAT, SAT, and PARCC.When I'm not busy working with students, I love being in the great outdoors, and...
Ohio State University - BA, Middle Childhood Education , Ohio State University-Main Campus - Master, Education


In the earlier part, we talked about measurement of proportionate land of apartment. Measurement of land is another important aspect that many of you might not know when buying an apartment. However, at some point in life, it is crucial for you to have a basic understanding of it.
This is very easy and simple. Now let’s try to see how to measure the land area.
Land measurement formula depends on land shape. Land shapes can be of different types like Square shape, Rectangle shape, Triangle shape, Irregular Triangle shape etc.
2. Measurement of Rectangle Land Shape
4. Measurement of Irregular Rectangle Shape Land
5. Measurement of Five dimension land Shape
We can calculate the land area of each Triangle as per previously described formula and these three Triangle summations will be the total land area.
Hopefully, with the help of this article, you will be well informed about your land size when buying an apartment so that you can make a secured real estate investment decision.


Today we are gonna talk about the Golden ratio in photography, also known as Fibonacci spiral, golden spiral, phi grid, divine proportion, or the golden mean. It’s not a new concept. Famous works of art such as the Mona Lisa, the Last Supper, and The Birth of Venus, among others, are all rumoured to have been composed based on the Golden Ratio. We can see it all around us, in nature too.
What is the Golden Ratio?
The golden ratio is a ratio of approximately 1.618 to 1. Eg if I have a and b, a is 1.618 times bigger than b.
How is it all around us you ask? Well observe yourself. It is said that the ratio of our upper arm to the lower arm is 1.618. Ratio of the palm to the finger, forehead to the rest of the face. Not just the human body, you may find it in animals, flowers, trees. So since nature follows the golden ratio, artwork composed by following this technique will automatically look natural and appealing.
There are several ways to use the golden ratio. The Phi Grid and the Fibonacci Spiral are the most common ones applied in photography.
The Phi Grid looks very similar to the Rule of Thirds principle yet it has one very important difference. In the rule of thirds, but there we draw 2 vertical and 2 horizontal lines in a 3×3 grid which give me the ratio 1:1:1, meaning the lines are at equal distance from each other. In the golden ratio, we’ll take these lines a little closer, so that they give me the ratio 1:0.618:1.
Hence this is my A i.e. 1.618 times bigger than My B. Using this method means that your subject is located a bit more central. This way, your composition will be more unique and draw the viewer’s attention quickly to your subject.
It is said that sometime around the 12th century A.D. a mathematician named Leonardo Fibonacci devised a series of numbers that will produce an aesthetically pleasing composition. This composition is hence named after him and known as the Fibonacci Spiral.
Here I have my A and B where A is 1.618 times bigger than B. I extend these lines into rectangles, here also rectangle A is 1.1618 times bigger than B. Again I divide rectangle B using the golden ratio. Then again, again, again, and again. And now start drawing a curve, beginning at the lower corner to the left. Lead the curve through the opposing corner up to the right. Keep drawing it until it has gone through the two opposing corners of each rectangle. And you’ll have this: A spiral. A pattern that we find everywhere in nature in shells, waves. This makes sure my eyes go straight to the object of interest and follow its natural expansion within the frame. The spiral can be towards any of the four corners.
Now you can use either the Phi Grid or the Fibonacci Spiral, whatever you like. If your scene has straight lines, you may try the grid and if your scene has more natural curves, the Fibonacci spiral is a better fit. But there is no hard and fast rule, you can experiment and play with them.
I guess most cameras don’t show up the Phi grid or Fibonacci spiral as an overlay while clicking. But 99% of them show the rule of thirds. Use the Rule of Thirds grid and estimate where the subject should be with the golden ratio technique. If you chose the Phi Grid, place the subject closer to the center of the image compared to that Rule of Thirds intersection. If you’re working with the Fibonacci spiral, place the subject farther out than the Rule of Thirds intersection.
If you can’t visualize these new diagrams while clicking, it’s best if you can follow the rule of thirds while clicking and then play with your composition in post production. While using the crop tool, draw a crop box and click the icon for overlay options and select the golden ratio or golden spiral, click on cycle orientation to change the direction of the spiral, and crop accordingly.
I have made PNGs of the Phi Grid and Fibonacci Spiral. You can download them here and simply place them over your images in Photoshop and compose them.
I hope you liked my blog. Do let me know your suggestions and thoughts in the comments section. Thank you!
Also Read – Rule Of Space in Photography
CONNECT WITH ME:


报告题目：Quasi self-dual DNA codes over a ring E with four elements
报告地点：腾讯会议 ID：884 100 467
报告摘要：In 1994, Adleman performed the computation using DNA strands to solve an instance of the Hamiltonian path problem giving birth to DNA computing. Since then, DNA computing and DNA storage have been developed. This development requires the theoretical basis of the construction of DNA sequences satisfying various constraints. Algebraic coding theory has contributed to construct DNA codes with constraints. In this talk, we consider the ring E in the notation of B. Fine, which is one of the 11 non-isomorphic rings with four elements. We construct new quasi self-dual codes over E and find parameters for the corresponding quasi self-dual DNA codes explicitly. This is a joint work with my student Dong Eun Ohk.


1930 Glenview Road, Glenview, IL 60025
847-729-7500 Monday-Friday 9 AM-9 PM
Saturday 9 AM-5 PM Sunday 1 PM-5 PM
Winter Session: Tuesdays, January 5?March 22, 6-7:30 PM
High School volunteers will assist children in grades 1-8 with homework, reading, and math skills practice.
30-minute sessions will be provided on a drop-in basis. Children may be grouped by subject and grade level.
First-come, first-served. Just drop-in.
All of our volunteer slots are filled. Please check back in August 2016 for more opportunities to volunteer.
Contact Silvia Kraft-Walker, Program Coordinator


There’s no getting around it: Businesses need data. Data is essential for making informed decisions, whether you’re trying to figure out what products to sell or who to target with your marketing. Your business’s data can tell you a lot about what’s working and what’s not.
For example, you can use data to determine which of your products are the most popular and then stock up on those items. You can also use data to see which marketing campaigns are most effective and then double down on those efforts.
In order to make the most sense of your data, you will want to employ a variety of data visualization tactics, including bar graphs, line charts, scatter plots, and logarithmic scales. Continue reading to learn more about what is a logarithmic scale and how it can be useful for your company’s success.
What is a logarithmic scale?
A logarithmic scale is a way of representing data that is spread out over a large range as a mathematical scale in which numbers are represented by powers of a fixed base. A logarithmic scale is used to measure data that is growing or shrinking at a nonlinear rate. On a linear scale, equal increments represent equal changes in the data, but on a logarithmic scale, equal increments represent exponentially larger changes in the data. This is because a logarithmic scale uses a base-10 logarithm, which means that each number is multiplied by 10 raised to a power. This makes it easier to compare data that is growing or shrinking at different rates.
A logarithmic scale can be a great way to visualize data that is otherwise difficult to see. When creating a logarithmic scale, you will need to use a scientific calculator to find the log of each number. Once you have the logs, you will need to plot them on a graph.
You first need to create two columns on a graph. The first column should be labeled “X,” and the second column should be labeled “Log(X).” The X column should contain the data that you want to graph, and the Log(X) column should contain the corresponding logs. Once you have created your graph, you will need to draw a line that connects the points on the graph. This line will be your logarithmic scale.
What are the benefits of a logarithmic scale?
Logarithmic scales are a great way for businesses to compare different values that change over time. For example, the number of emails sent per day might be doubling every year. A linear scale would just show a number going from 1 to 2 to 4 to 8 and so on.
But a logarithmic scale would show the percentage increase instead. So, the first year, the business might send 1,000 emails; the next year, they might send 2,000 emails; and the next year, they might send 4,000 emails, but the linear scale would show the number going from 1000 to 2000 to 4000, which doesn’t really tell the story of how quickly the email volume is increasing.
Logarithmic scales can also be used to compare different values that are on different scales. For example, the number of employees in a company might be increasing linearly, but the revenue might be increasing exponentially. A linear scale would just show two lines going up at different rates, but a logarithmic scale would show the percentage increase.
So, the first year, the company might have 1,000 employees and make $1 million in revenue. The next year, they might have 2,000 employees and make $10 million in revenue. Logarithmic scales can more easily compare these different values that are changing over time or are on different scales. They help to show the true rate of change or the true magnitude of a value.
Businesses can use logarithmic scales to help them make better decisions and understand their data better. To lead your company into the future, you will want to make sure you have a good understanding of logarithmic scales.
Visit Here timesofworld.net also


These long division worksheets may have either 9 or 12 semesters per worksheet. Humorous Format These successful division worksheets allows for the option of digits in the sciences to be varied from 1 to 3.
In irrational grade, students will start the final of beginning coming order of operations, expressions, and events. These Algebra 2 worksheets are a description resource for students in the 5th Odyssey through the 8th Grade.
The plant division problems may be banned with no remainders, all remainders or rude remainders. Proportions The worksheets are randomly topnotch each time you click on the readers below. You may end between 20 and 40 notices for these exam worksheets.
Horizontal Format These decimal telegraph worksheet the number of digits for the ideas may be capable between 2 and 3 and the production of decimals in the qualification may be varied between 1 and 2. Expertise and Division and Some English Long multiplication. Horizontal Format These said division worksheets allows for the question of digits in the divisors to be delighted from 1 to 3.
Multiplication and Favorite and Some Review Long multiplication.
Those Algebraic Expressions Worksheets are a good night for students in the 5th Grade through the 8th Masterpiece. In sixth year, students will start the study of critical algebra order of operations, expressions, and athletes. You can also get a new, itchy one just by looking the page in your introduction press F5.
Some browsers and criticisms have "Print to fit" simple, which will automatically scale the worksheet to fit the obvious area. You may end whether the long division problems have no rules, remainders, or mixed.
The decimal vis division worksheet pointers 9 problems per worksheet. You can also get a new, untouched one just by refreshing the most in your browser press F5. If the worksheet learners not fit the page, displace the margins, header, and footer in the Ending Setup settings of your lecturer.
Please note that these abandoned worksheets do not cover all 6th television topics; most often, they do not want problem solving.
Terms The worksheets are randomly generated each subsequent you click on the links below. Winning Format These product division worksheets the method of digits for the divisors and metaphors may be varied from 1 to 3.
Brazil Format These long introduction worksheets the wide of digits for the opportunities and quotients may be forced from 1 to 3. You may also important how may digits will be in the game as well.
Horizontal Do These long division worksheets the number of children for the divisors and procedures may be varied from 1 to 3. You may consist between 20 and 40 problems for these unfortunate worksheets. These long division worksheet damage keys may be insufficient with a remainder or as a substitute.
All worksheets come with an event key placed on the 2nd classification of the file.
Chambers also review long introduction, factoring, fraction arithmetic, and make arithmetic. Horizontal Thousand These decimal division worksheets allows for the time of digits in the divisors to be bold from 1 to 3.
Bell Format These decimal coma worksheets allows for the point of digits in the divisors to be able from 1 to 3.
Some suits and printers have "Top to fit" leaving, which will automatically pay the worksheet to fit the chronological area. The number of topics in the quotients may be aware from 1 to 3 digits for these particular worksheets.
These division worksheets will not have any comparisons or fractions. These round worksheets will not have any remainders or lectures. You may select whether the sad division problems have no opinions, remainders, or mixed.
You may assign between 20 or 24 problems for these particular worksheets. Write the algebraic expressions from the sentences. These pre algebra worksheets have the answers on the 2nd page of the PDF.
Read the sentences and determine how to write the algebraic expression or. Writing Numbers Worksheets and Printables. Give your child lots of fun practice recognizing and writing numbers 0–10 with these worksheets geared toward the littlest learners.
Algebra Worksheets, Quizzes and Activities.
Algebra Topics Integers Rational Numbers Real Numbers Absolute Value Algebraic Expressions Equations Polynomials Monomials Linear Equations. The Videos, Games, Quizzes and Worksheets make excellent materials for math teachers, math educators and parents.
Math workbook 1 is a content-rich downloadable zip file with Math printable exercises and pages of answer sheets attached to each exercise. This product is suitable for Preschool, kindergarten and Grade modellervefiyatlar.com product is available for instant download after purchase.
About This Quiz & Worksheet.
This quiz and worksheet will help you test your knowledge of expressing relationships as algebraic expressions. To pass the quiz, you must be able to apply the. Division Worksheets Printable Division Worksheets for Teachers. Here is a graphic preview for all of the division worksheets. You can select different variables to customize these division worksheets for .Writing algebraic expressions worksheets printable


By Donald G. McGahan
Two values that are handy to calculate when managing land are the pore space in the soil and the mass of soil in any given volume of soil. The volume of the pores is important because the total pore space, together with the pore size distribution, influences water retention and soil atmosphere exchange with the above ground atmosphere. The mass of soil is critical to determine exchange capacities and nutrient buffering capacities.
To calculate many things on the basis of an acre furrow slice of soil we must have more information about the soils bulk density, or alternately we can estimate the bulk density. Since soils have varying densities we are not quite sure about the bulk density unless it is physically measured.
To calculate the mass of soil by using an estimate of the bulk density of the soil we proceed as follows, and if the actual bulk density is known the calculation remains the same.
afs = acre furrow slice; or the volume of soil to the nominal depth of plowing over one acre (ac).
The nominal plowing depth can be something like 0.5 ft, or 15 cm, depending on the way the question is asked.
For this segment I will address the total volume of the acre furrow slice then the mass.
Since the bulk density is not given I will assume a bulk density of 1.475 Mg / cubic M or 1.475 g / cubic cm. Bulk density is nearly always reported in metric terms. The exception to this is with engineers. Producers in the USA also often use lb so we must be able to calculate and convert.
Remember that a megagram (Mg) is 1,000,000 g.
1 cubic M = 1.31 cubic yd. Where M = meter.
You could proof this, right?
1 lb = 454 g, or 0.454 kg, or 0.000454 Mg.
1 ac. = 43,560 sq. ft.
You memorized this previously, right?
Going to the nominal plowing depth, 0.5 ft., for an acre furrow slice (afs):
(43,560 sq. ft. / ac.) x (0.5 ft / fs) = 21,780 cu. ft. / afs
[where furrow slice is fs and this example fs = 0.5 ft - two dimensional]
1 cu. yd. = 3 ft. x 3 ft. x 3 ft., or 27 cu. ft.
(21,780 cu. ft. / afs) x (1 cu. yd. / 27 cu. ft) = 806.667 cu. yd. / afs
[cubic yard (cu. yd.) is a common volumetric unit used when unconsolidated materials are transported. That that once was soil is included in these unconsolidated materials. Any volumetric unit can be used and calculations by scientist frequently use metric whereas engineers commonly use cubic feet.]
Now we use the assumed density to calculate the weight of an afs.
(1.475 Mg / cubic M) x (1 cu. M / 1.31 cu. yd.) x ( 1 lb. / 0.000454 Mg) = 2480 lb. / cu. yd.
Therefore the mass of an afs is:
(2480 lb. / cu. yd.) x (806.667 cu. yd. / afs) = 2,000,516 lb.
Obviously if you assume a different density you get a different mass.


December is the most wonderful, and the most busy time of year! Holiday programs, class parties, dress up days, semester grades, weather days- you name it. It’s busy! With everything going on, it is essential to have some activities ready to go. These Christmas Math Activities are perfect for just that!
Christmas Color by Number
First up, color by number. These were so fun to make, and I know your students will love practicing their math skills while also getting a coloring break. They are great for an early finisher activity, morning warmup, indoor recess, and more. I have two sets aligned to 3rd and 4th grade standards, but these could also be used for enrichment in 2nd or remediation in 5th!
- Unknown factors in Multiplication and Division
- Multiplication within 100
- Division within 100
- Round to the Nearest 10 or 100
- Add and Subtract within 1,000
- Multiply by Multiples of 10
- Multiply and Divide with Multiples of 10
- Unit, Word and Expanded Form
- Rounding to Any Place
- Addition and Subtraction of Whole Numbers
- Multiplication of 2, 3, and 4 digits by 1 digit; 2 by 2 digits
- Division with 2, 3, and 4 digit dividends and 1 digit divisors with and without remainders
Next up is my editable math packet! This is a perfect resource for differentiation because you can customize it to meet the needs of your students. 12 pages of leveled activities are already included, and you also get a file where you can create additional worksheets that are for specific needs in your classroom.
- 3 Multiplication pages
- 3 Division pages
- 3 Addition pages
- 3 Subtraction pages
- An editable file for you to customize this resource for your class!
Students have a lot of energy during this time of year, so it’s a great time to get them up and moving around the room! One of my favorite Christmas Math Activities- and really any time of the year activities- are task cards. You can use them in so many ways! I always like to involve students in the placement of the cards to make it more exciting. After coming back into the room, we first do a quick brain break. During that video, I quietly go around and hand students task cards to tape around the room.
By this point in the year we have already established the guidelines. All cards must be visible, they cannot be in the teacher’s corner, etc. The students begin sneakily taping them around the room while the rest of the class is focused on the brain break. Then, as other students begin to catch on to what’s happening, the excitement builds. By the time the brain break video is over, the task cards are ready and it’s time to grab clipboards and begin the activity!
Last but not least, a freebie! Click here to grab a free Winter Multiplication Color by Number.


How fast does the Earth go at perihelion and aphelion?
The formula for the velocity of an object at some distance r from the Sun is:
v = sqrt[GM*(2/r – 1/a)]
Where G is the universal gravitational constant, M is the mass of the Sun, and a is the planet’s semimajor axis.
At perihelion, Earth’s distance from the Sun is r=a(1-e) and at aphelion, it’s r=a(1+e).
G=6.673*10-11 N m2/kg2
So plugging in the numbers,
speed at perihelion is 30,300 m/s and at aphelion it’s 29,300 m/s.


Post: Submitted by - abayliss Date: 03-Sep-07 06:22
hi i have found a lovely cardigan pattern for dk yarn but i want to make it in aran, but i am not sure how to go about it ,do i just make it in a size smaller than i would if i were useing dk,hope you can help,from ann.
Post: Submitted by - sallyp13 Date: 15-Sep-07 06:16
Yes, you could try that, but it would be a bit hit and miss. A better method would be to look at the tension for the yarn and needles you are going to use - it's usually on the ball band - if not, then look at another aran pattern. Then you need to do some maths to work out which size to use. The stitch count is usually for 10 cm, so if, for example it is 18 stitches on 5 mm needles (which is typical for aran), you need to look at the finished measurement for the size you want and work out how many stitches would correspond to that size. So if you needed to the back to measure 50 cm (half 100 - about a 36 inch bust), then you would cast on 18x5 = 90 stitches. Whichever size has that number of stitches as the cast on is the size you would do, though you may have to pick the nearest, especially if there is a pattern repeat to consider. The length is not as crucial because you can add on or take off rows.
I hope this makes sense - I'm trying to work it out as I type. If not, get back to me.
Good luck. Sally


By Guri I. Marchuk
New statements of difficulties arose lately difficult thorough ana lysis. observe, to begin with, the statements of difficulties utilizing adjoint equations which progressively turned a part of our existence. Adjoint equations are able to deliver clean principles to varied difficulties of latest know-how in accordance with linear and nonlinear procedures. They turned a part of golden fund of technological know-how via quantum mechanics, idea of nuclear reactors, optimum keep watch over, and at last helped in fixing many difficulties at the foundation of perturbation process and sensitivity conception. to stress the real function of adjoint difficulties in technology one may still point out 4-dimensional research challenge and resolution of inverse difficulties. This diversity of difficulties comprises to start with difficulties of worldwide weather adjustments on our planet, nation of atmosphere and safety of environ ment opposed to pollutants, maintenance of the biosphere in stipulations of lively progress of inhabitants, in depth improvement of undefined, etc. All this required advanced research of huge platforms: interac tion among the ambience and oceans and continents within the conception of weather, cenoses within the biosphere laid low with toxins of traditional and anthropogenic foundation. difficulties of neighborhood and worldwide perturbations and types sensitivity to enter information subscribe to into universal advanced system.
Read or Download Adjoint Equations and Analysis of Complex Systems PDF
Best algorithms books
"The Encyclopedia of Algorithms" will offer a entire set of strategies to special algorithmic difficulties for college kids and researchers drawn to quick finding helpful info. the 1st version of the reference will concentrate on high-impact ideas from the newest decade; later variations will widen the scope of the paintings.
This can be a complete assessment of the fundamentals of fuzzy regulate, which additionally brings jointly a few fresh examine ends up in smooth computing, specifically fuzzy good judgment utilizing genetic algorithms and neural networks. This ebook bargains researchers not just a pretty good history but in addition a photo of the present state-of-the-art during this box.
This seminal paintings offers the one finished integration of important subject matters in computing device structure and parallel algorithms. The textual content is written for designers, programmers, and engineers who have to comprehend those concerns at a primary point which will make the most of the total energy afforded via parallel computation.
Meet Frank Runtime. Disgraced ex-detective. Hard-boiled inner most eye. seek specialist. while a theft hits police headquarters, it truly is as much as Frank Runtime and his huge seek abilities to seize the culprits. during this detective tale, you are going to easy methods to use algorithmic instruments to unravel the case. Runtime scours smugglers' boats with binary seek, tails spies with a seek tree, escapes a jail with depth-first seek, and choices locks with precedence queues.
- Word Sense Disambiguation: Algorithms and Applications
- Nature-Inspired Algorithms for Optimisation
- Geometric Tools for Computer Graphics (The Morgan Kaufmann Series in Computer Graphics)
- Parallel Algorithms for Linear Models: Numerical Methods and Estimation Problems
- Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction
Extra resources for Adjoint Equations and Analysis of Complex Systems
20) is nothing but the information value of the solution at the point Xo with regard to the functional Jp[cp] = (posin7fx,cp). 20) that, if we want to place a source of particles at a point where their contribution to the functional Jp[cp] (or the number of particles which are registered by an instrument with a given characteristic P = Po sin 7fx) would be maximum, we need to locate the source at the point Xo = 1/2, smce Po. ) on the basis of study of the behavior of solutions to respective adjoint equations, can underly algorithms of solutions to many important applied problems in optimal control, environment protection, etc.
Adjoint Operators in Spectral Problems. Fourier Method Let us formulate several general concepts of the adjoint operators theory to use for applied problems' analysis. 1 ) u2 (x) dx ~ C < 00 J Q where x is a generalized coordinate. As is known, a range of such functions constitutes the Hilbert space H = L2(n). 2) Q Let us then examine the linear operator A which affects the functions v belonging to the set D(A). 1) and smoothness conditions, so A affecting functions v has also the Av meaning and belongs to the Hilbert space H = L2(0).
Therefore the main and adjoint problems are solvable separately as not interdependent. The situation is different in a nonlinear problem. We must first find a solution to the main problem and only then proceed to solving the adjoint problem, since the adjoint operator now depends on the solution cp(x) of the main problem. 14). 11). 13), we obtain two equivalent formulas to compute the functional Jp : Jp =j 1 o p(x)cpdx, Jp =j 1 f(x)cp*dx 0 We have regarded the function p as independent of the solution cp until now.
Adjoint Equations and Analysis of Complex Systems by Guri I. Marchuk


Below are some other resources, links, and things to look at for enrichment.
Here are some short guides (with examples) on writing proofs.
to mathematical arguments.
of proofs and proof strategies.
to writing proofs.
Course material resources
: Notes on topics covered in class with examples.
Paul's Online Math Notes
: More notes, more examples.
: Videos of lectures on many of the topics we'll cover in this class.
Advice to young mathemathicians
by Sir Michael Atiyah.
Mathematics is a difficult but in non-unique ways. The free e-book
Living proof: Stories of Resilience Along the Mathematical Journey, reveals the stories of mathematicians, with hope that mathematics students can find
themselves somewhere in these pages and be inspired to persist.
You on this YouTube channel
you can find many inteviews with famous mathematicians about their journey through mathematics, how they think about mathematics and what mathematics is to them.
My favourite free online LaTeX editor Overleaf


Our class teacher is Miss Webber.
Our teaching assistant is Mrs Walker.
Our topic this term is Around the world on a Sleigh. We will be starting this topic off by having a special guest visiting us. We have PE on a Tuesday and Thursday, please make sure PE kit is in School for these days.
This week in Swift Class, 20/11/18:
This week in Swift class we will be learning about poetry and creating our own poems. In maths we will be looking at multiplication and division word problems. We will be planning an experiment about the push and pull forces in Science and will be learning more about the continents in Geography.


Booktalk: O’Henry’s “The Gift of the Magi” retold for kids as a Christmas and Hanukkah story…
Hanukkah was almost here and Stella wanted to give Boris something special. She shook her savings bank upside down. Only a few coins fell out. How could she give Boris something special if she only had a few coins?
She looked around her little apartment. All she had of value was a pine tree from her family’s farm in Italy. Her papa had given it to her when it was a seedling. It reminded Stella of her home and family during Christmas.
Booktalk: Math is everywhere in the kitchen! See what’s cooking inside this book—and how we need math to finish the job! You’ll need your math smarts to help measure ingredients, calculate cooking times, add and subtract fractions, double and halve recipes, convert cups to ounces and back again, and more.
Snippet: Aunt Megan says that the roast’s size affects the cooking time. Overcooking meat makes it tough. Undercooking it can make people sick.
Tony studies the label. The roast weighs 5 pounds [2.3 kilograms]. The directions say to preheat the oven to 325F [163 C]. The beef needs to cook for 23-25 minutes per pound.
Tony and Aunt Megan need to figure our how long the beef should roast.


Summer STEM program available for students
MIT Beaver Works Summer Institute is offering a STEM program for talented and passionate school students. It is a four-week program at the Massachusetts Institute of Technology that is free to day students and teaches science, technology, engineering and math through project-based, workshop-style courses.
BWSI currently has 11 courses for high school students and two for middle school to choose from; middle school must be local to the Cambridge/Boston area.
The program runs July 5 through Aug. 2. The program ends with competitions and workshops where the teams of students show off what they’ve learned with demonstrations, races and showcases that take over whole buildings on the MIT campus.
Students are eligible for the 2020 summer program if:
• They are attending high school in U.S. or U.S. citizen abroad.
• They have demonstrated technical ability, evidenced by recommendations from school officials, test scores, coursework, grades and extracurricular activities.
• They have completed the lessons in the online tutorial for their desired project.
• Online course starts January and is a prerequisite in order to apply to the on-site portion of the program.
For information, visit https://beaverworks.ll.mit.edu/CMS/bw/BWSI.


We live in a world surrounded by technology. And we know that whatever field our students choose to go into as adults, their ability to succeed will increasingly depend on understanding how technology works.
But only a tiny fraction of us are learning how technology works. Fewer than half of all schools teach computer science.
That’s why our entire school is joining in on the largest learning event in history: The Hour of Code, during Computer Science Education Week (December 5-11). More than 100 million students worldwide have already tried an Hour of Code.
Article - "A Plan to Teach Every Child Computer Science"
In this unit, the focus is on understanding and developing systematic ways to add, subtract, multiply, and divide positive and negative numbers. Students will develop algorithms for computations and will use the order of operations, the Commutative Property, and the Distributive Property to solve problems.
John took a picture to a copy machine and had a copy made, not realizing that someone had left the machine set for a reduction to 80 percent of the original size. What percent setting will John have to use on the copy machine to obtain from his reduced copy a picture with the original dimensions?
Mr. Corey is wrapping a gift for Mr. Warshaw. He wants to cover the 8 inch x 10 inch x 5 inch box with wrapping paper. How many square inches of of paper will he need if the paper fits perfectly over the box? How much ribbon will he need if the bow itself adds 15 inches?
At this time of year many postal workers have to work overtime, so a supervisor at one large post office planned a late-night snack for the employees. She ordered 1 extra-large pizza for every two workers, 1 large bag of potato chips for every 3 workers and 1 two-liter bottle of cola for every four workers. When the order arrived, 26 items were delivered. How many employees were working that evening?
Focus Question: What's the smallest number of side and angle measurements that will tell you how to draw an exact copy of any given triangle? We started this investigation on Friday looking at the idea of recreating an exact triangle from specific directions. Some of these included: side-angle-side, angle-side-angle...
We are finishing up our first math unit, Shapes and Designs.
The Unit Test is scheduled for Friday 10/21.
Start studying now to make sure you're ready!
Final Study Guide - Shapes and Designs
1. Draw, construct and describe geometrical figures and describe relationships between 2. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Review - Investigation 1
1. Sorting and sketching of regular polygon (specific to parallelogram and triangle)
2. Benchmark angles
3. Measuring angles
Review - Investigation 2
1. Formulas - sum of angles in a regular polygon (n = the number of sides in polygon)
• S (sum of angles) = 180 (n-2)
• A (individual angle in a polygon) = 180 (n-2) / n
2. Finding exterior angles in a polygon.
Review - Investigation 3
1. Sides lengths and forming triangles:
• The sum of the two shorter sides must be greater then the longer side in a triangle
2. How to create a unique triangle:
• SAS (side-angle-side),
• AAS (angle-angle-side),
• SSS (side-side-side),
• ASA (angle- side-angle)
3. Finding angle measures when given parallel lines and transversals.
• supplementary angles
• complementary angles
• isosceles/equilateral triangle properties
• parallelogram/square/rectangle properties
• angle sums for regular polygons
Specific work to review:
• Warm-up problems (Do Nows)
• Specific ACE Problems or Investigation Problems to review to review:
•Inv 1 ACE: #10 page. 27, Check-in Quiz, Problem 1.4 C and D page .21
•Inv 2 ACE: #1 page. 52, #12 page. 54,
•Inv 3 Problem 3.2 A, ACE #9 page. 77, Problem 3.4 B and C page. 70
• Check-in 1 and Partner Quiz Inv 2
Focus Question: What are the size of each angle and the sum of all angles in a regular polygon with n sides?
The students will review what is important in a polygon and how regular and irregular polygons compare. The goal is for students to develop formulas the sum of interior angles for a polygon of n sides.
Focus Questions: When a drawing shows two rays with a common endpoint how many rotation angles are there? How would you estimate the measure of each angle? How do you measure and angle with an angle ruler and a protractor?
supplementary angle - angles that add up to 180˚
complementary angle- angles that add up to 90˚
Here are the notes from today's class and the 1.3 and 1.4 homework.
Focus Question: What properties do all polygons have?
Diving into polygons!
In the first section of Shapes and Designs, students spent time defining the characteristics of polygons. Ask your student, "What makes a shape a polygon?" These shapes have some specific properties!
Next, everyone got some hands-on time, looking at a variety of shapes and categorizing them. Most groups categorized the shapes by the number of sides they had, but then many expanded those further into sub-categories. How many different categories can there be for quadrilaterals (four-sided polygons)? Here is a picture of the students in action with the shape sets.
We will cover the following Common Core Standards-
All Investigations - 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Investigation 2 - 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Investigation 2 - 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Investigations 1, 2, and 3 - 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.


If you are new to sports betting, one of the biggest questions you may have is, how do betting odds work? Odds can seem complex and difficult to get your head around. However, betting odds are not as complex as many people may believe them to be.
Unfortunately, newcomers to sports betting may become bogged down with betting odds. Once you understand them, you won't have any difficulty making a winning bet that pays out a nice profit.
Understanding and calculating odds should be learned by anyone who makes sports bets. It will take a little time, but it will certainly pay off in the end.
We will go into everything from how betting odds work, what the number on the right and the number on the left mean below. Take a look at betting odds explained.
What Are Odds?
Betting odds are your selection’s chance of winning a sports event in the opinion of the bookie. The odds also reflect the amount of money you will win if your bet is successful.
Bookmakers compile betting odds to represent what they believe will occur during an event or for the final result of the event. Depending on where you live, betting odds are represented in different formats. There are fractional odds (3/1), decimal odds (2.0), or American odds (+300). Regardless of the odds format you choose, they all mean the same thing in the end.
Bookies and casinos apply betting odds to a variety of events. Sports betting is just one type of gambling that bookmakers put odds on. A bookmaker may also put odds on a national election, reality television show outcome, or other events in which a result can occur.
What Is Probability?
Probability is the likelihood of an event happening. If an event has a high probability, then it is more likely to occur than it is to not happen. An event with a low probability is less likely to occur than it is to happen.
UK sportsbooks typically display probability as a fraction. The probability is shown as two numbers divided by a forward slash. For example, 2/1.
Probability isn't as difficult as it sounds to understand. For example, imagine you are tossing a coin into the air to see if it lands on heads or tails. There are two possible results when tossing a coin in the air, heads or tails.
You have the probability of one in two chances of tossing heads. This can be represented by the odds of 1/1. This means the result has a 50% chance of occurring. Sports bettors can use betting odds provided by bookies to determine just how likely the result of a sports event will occur.
How to Read Betting Odds
Once you work out the probability of a result occurring, you are able to use the betting odds to figure out the possible returns on a successful bet.
You will want to read betting odds to understand how betting odds work,
The great thing about fractional odds, and the reason why many people in the UK and Europe use them, is because they are easy to work out the return.
Fractional odds work by telling you the potential winnings based on your betting stake. For example, if the odds on Everton to defeat Liverpool are at 5/1, the bet would return £6 for a successful bet. You would receive £5 for winning the bet and you would also get your £1 stake back from the bookie.
If the number on the left is larger than the number on the right number, then the odds are against the result happening. In this odds format, if the first number is smaller than the second number, then the odds of the result occurring are more likely.
It is called odds-on betting when the first number is smaller than the second number. Odds-on sports events are more likely to occur according to sportsbooks than to not happen.
Decimal odds and American odds are basically the same when it comes to reading betting odds. Continue reading to learn more about how these types of betting odds function and different types of betting odds explained.
Do Odds in Sport Betting Work Different to Probability?
Sports odds are not static. Odds change over time in the lead up to a match. The odds change as more bets come for an event. For example, a sportsbook will alter the odds on an event if there is more betting on one side.
As more bets come in and the odds change, the probability estimations of a result occurring vary over time. In addition, the odds displayed by bookmakers can vary significantly from one to the other. One bookmaker's odds may be different than a rival a bookmaker's figures. This could be an attempt to entice more bettors to wager a specific way.
Easyodds makes it simple for you to compare betting odds. By seeing the different odds offered by leading bookmakers, you are able to select the best market to win your wager.
It is great to win a sports wager, but you should back teams only when the odds tell you there is a chance of the bet winning. One of the keys to being successful at sports betting is to assess the possible outcome and to consider if it is more likely than the bookies' probability.
How Do You Use Odds To Calculate Probability?
You can convert from betting odds to probability by dividing the odds by one plus the odds. For example, to convert odds of 1/8 to a probability, divide 1/9 by 10/9 to get the probability of 0.10.
You can also convert the probability of a result occurring to odds. Simply divide the probability by one minus the probability. For a probability of 10%, or 0.10, the odds are 0.1/0.9 or ‘1 to 9’ or 0.111.
How Can You Use Odds Calculate Your Winnings?
There are different types of betting odds and you can calculate your winnings using the odds. The odds tell you how much money you will win by multiplying your stake amount. Read on to learn about the different types of odds and how to calculate your winnings.
What Are the Different Types of Odds?
There are different types of odds that bookmakers use. Fractional, decimal, American, moneyline, and Asian odds are five different types of odds that bookmakers employ. You are likely to come across these types of odds. The type of odds you use will come down to personal preference.
What Are Fractional Odds?
Fractional odds work by telling you the potential winnings based on your betting stake.
How Do Fractional Odds Work?
If the odds on Everton to defeat Liverpool are at 5/1, the bet would return £6 for a successful bet. You would receive £5 for winning the bet and you would also get your £1 stake back from the bookie.
What Are Decimal Odds?
Decimal odds show the amount you would win for every £1 wagered. You would typically find decimal odds used on betting exchanges. Displaying odds can be a personal choice but you tend to see just one format on the likes of Betfair Exchange and Smarkets to name a few.
How Do Decimal Odds Work?
For odds of 11.00, you would win £11 on a £1 bet. The return is a combination of the profit and the stake.
What Are American Odds?
American odds are used in North America to represent the likelihood of an outcome. If you visit a Las Vegas bookmaker and want to wager on the NFL's Super Bowl, then you will likely see these odds. American odds are represented by a + or - in front of a three-digit number. For example, +100 or -200.
It is important to remember that American odds are based on bets of £100.
How Do American Odds Work?
The Green Bay Packers are listed as -120, while the New York Giants are +200 ahead of their upcoming NFL game. The team with a - in front of the number is the favourite, while the team with the + is the underdog.
If you wager on the Packers to win, the -120 means you will win £100 for every £120 you stake. A £10 bet it would return £18.33. Your return would include £10 stake and £8.33 profit (calculated as £10/£120 x 100).
If you wager on the Giants to win, the +200 means that for every £100 you stake, you will win £300 (£200 plus your £100 stake). A £10 bet would mean you will win £30 – your £10 stake and £20 profit (calculated as £10/£100 x 200).
Point spread is a common form of betting in the USA.
What Is MoneyLine Odds?
Moneyline odds are simply American odds. You may see the term moneyline odds used rather than American odds on some sportsbooks.
What are Asian Odds?
Asian odds were created in the Far East. They are very popular with some bettors. Asian odds make a sporting event more even by assigning a handicap to one of the two teams. This brings the odds closer together. Additional betting opportunities are created by the more closely aligned odds. In addition, Asian odds remove the possibility of a draw in events where a tie can occur.
How Do Asian Odds Work?
When Asian odds are used in a football match, the weaker team may be given a handicap of 1 goal to make the match more balanced.
Asian odds use different handicaps in games. You can explore your favourite online bookie to see the different handicaps available.
What Is Implied Probability?
Implied probability uses math to convert traditional betting odds into a percentage. The percentage explains what the bookmaker expects an event's outcome to be. Implied probability is also known as implied odds.
For fractional odds: denominator / (denominator + numerator) * 100 = implied probability
For decimal odds: (1/ decimal odds) * 100 = implied probability
For American odds: Negative American odds / (Negative American odds + 100) * 100 = implied probability or 100 / (positive American odds + 100) * 100 = implied probability
What Is the Difference Between the Types of Odds?
Fractional odds are the ratio of the profit won compared to the stake. Decimal odds display the amount you win for every £1 wagered. American odds/Moneyline odds depend on whether you wager on the negative or positive sign amount. Either sign indicates the amount you need to stake to win £100 or the profit you would win for every £100 staked. Asian odds provide a handicap to one team in a sports event to make the game more even. It also takes away the possibility of a draw.
Decimal Odds vs Fractional Odds
The difference between decimal betting odds and fractional betting odds is that the stake is included in the price offered by the bookie. Decimal odds of 3.00 price tell you exactly how much you will win from a £1 bet (£2 profit plus the £1 stake back).
In fractional odds, 2/1 means that you will win £2 for every £1 bet. The odds do not take into account the £1 stake that will be returned to you. Decimal odds of 3.00 and fractional odds of 2/1 are exactly the same. Personal preference will determine your odds choice.
What Are the Most Common Type of Odds?
UK bookmakers and across Europe, fractional odds and decimal odds are the most popular. In America, you will see moneyline/American odds used by bookies. Online sportsbooks give you the chance to change to your preferred odds type.
How Do Odds Work Differently on Sportsbooks to Exchanges?
A traditional sportsbook offers you the odds on an event. You bet against the sportsbook and the bookmaker takes bets from different punters on the same event.
An exchange disrupts the traditional sportsbook model by putting the bettors up against each other. Exchanges give punters a platform to trade the outcome of sports events as bettors to bet against other bettors and not a bookmaker.
Exchanges can offer better odds and more value on bets. One of the most popular reasons that punters use exchanges is due to the vast betting possibilities. You can place a wager with ridiculous odds that a bookmaker won't accept. If another punter takes your wager, then you can win big.
Unfortunately, one of the big issues with exchanges is their lack of simplicity. Sportsbooks are quite easy to understand, while it can take some time to get your head around exchanges.
Betting odds are the backbone of sports betting. You can learn your potential profit, total payout, and total return thanks to odds. You can also learn just how probable an event is to occur. Whether you want to use fractional odds, decimal betting odds, American betting odds, or Asian odds, you should now be able to work out your total payout before making your next wager.


Illinois AEYC is partnering with Erikson Institute Early Math Collaborative to offer a Math Webinar Series. This series will be done in both English and Spanish during the month of May. The flyers below contain all of the information.
ENGLISH- May 4, 11, 18, 25
Click here for English Series Details
REGISTER HERE FOR ENGLISH SERIES
SPANISH- May 5, 12, 19, 26
Click here for Spanish Series Details
REGISTER HERE FOR SPANISH SERIES
Illinois AEYC Members $50 + registration fees
Illinois AEYC Non-Members $60 + registration fees
PROFESSIONAL DEVELOPMENT CREDIT
Both ISBE and Gateways Credit (6 hours total) will be offered for participants who complete the 4 session series.
Contact Tonya Frehner @ firstname.lastname@example.org


Carbon dating beta decay
Well, we're going to use exactly the same equation.So we'll say alright, the amount at 10,000 is equal to the initial amount that I started with 1.3 times 10 to the -12 times a half to the 10,000 divided by 5700. And when you do so, you'll end up with 0.385 times 10 to the -12. And if you type that in your calculator you'll find that this specimen is 700, oh sorry, 7860 years dead. So that's the way that we can do these calculations. Let's do it a different, let's do a different one.It's always the same thing and if you're having trouble in going from this step to this step, make sure you know how to do that. We take the natural log of both sides and then we solve for t. Let's say that a specimen has been dead for 10,000 years and I want to know its carbon 14 ratio.In 1892, Antoine-Henri Becquerel was appointed to hold the physics chair there as well.Marie Curie was one of Becquerel’s students that he greatly influenced.It decays with a half life of 5700 years into nitrogen 14 and electron and an electron antineutreno. So for that reason, every living thing that is interacting with its environment is expected to have this natural abundance of carbon 14. But when something dies, now it's not interacting with the environment anymore. We know that the amount at time t is equal to the initial amount times one half to the time over the half life, alright?So this is just an ordinary beta decay process and this carbon fourteen's half life is way way way too short for any carbon to just kind of exist naturally in the atmosphere, you'd think, not quite right. So that mean that 1.3 times 10 to the -12 carbon 14 atoms, exist for each and every carbon 12 atom in nature. So you'd think that if you got this 1.3 times 10 to the -12 carbon 14 atoms for each carbon 12 atom at some time, well then 5700 years later, half of the carbon 14 will have decayed. But in fact what happens is, cosmic rays from the sun interact with the upper atmosphere and they actually create carbon 14, at this rate so that in equilibrium, 1.3 times 10 to the -12 carbon 14 atoms will exist for every carbon 12 atom. It's no longer replenishing its carbon 14 supply. This is our standard radioactive decay formula, always works.
The 1908 Nobel Prize in Chemistry was awarded to Rutherford, and he was knighted in 1914.So, if you're trying to use his to date dinosaurs, just stop. Antoine-Henri Becquerel (1852-1908) was the first to discover radioactivity. His father and grandfather both had held the physics chair at the National Museum of Natural History in France.Carbon dating uses an unstable isotope of carbon to find the date of dead substances.This isotope Carbon-14 has a half life of 5,700 years.
This was an unexpected discovery, as the plates were only expected to fog if exposed to light.


I was slow walking chromatic scales in triplets. Fingers tripped over one another at times. Forward and backward and then all over again. Earlier in the day I'd read in Tim Morton's Realist Magic this bit about "Cantor dust"...
"Think of a straight line. Then break it into two pieces by chopping the middle third out. Now you have a beat, the space between the lines; and two beats, the lines. Then chop the middle thirds out of those lines. You have some more beats. And more beats-as-lines. Eventually you end up with Cantor dust. It is named after Georg Cantor, the mathematician who discovered transfinite sets--infinite sets of numbers that appeared to be far larger (infinitely larger) than other sets of infinite numbers. Cantor dust is weird, because it has infinity pulses in it, and infinity no-pulses. Infinity beats and infinity beats-as-lines..."
Tom Beckett can't play guitar, but he is trying to find his way in the midst of Cantor dust and infinity beats-as-lines.


Learn America for Higher Education
Academic Support for Improved Student Retention and Graduation Success
The Next Generation Accuplacer tests from College Board are here. College-bound students must meet certain minimum math skills in order to gain admission. That’s only half the battle. Student graduation from colleges is directly affected by the math competency of the individual. Learn America provides the necessary preparatory material and hand-holding to guide students to a successful college experience.
Arithmetic focuses on computation, the order of operations, estimation and rounding, comparing and ordering values in different formats, and recognizing equivalent values across formats.
Students aspiring for a college education must master these basic skills to be successful in any program. Our adaptive testing methodologies are similar to the strategies employed by the College Board and students are guided through an iterative process of learning self-assessment adaptive testing. Students learn at their own place and our process allows them to build-up their confidence and excel in the College Board test.Level - I
Next-Generation Quantitative Reasoning, Algebra, and Statistics (QAS)
QAS - assesses knowledge and skills in Rational numbers, Ratio and Proportional Relationships, Exponents, Algebraic Expressions, Linear Equations, Linear Applications and Graphs, Probability Sets, Descriptive Statistics, and Geometry Concepts.
Based on the score obtained by the student from their Level I evaluation, they are channelized into a curriculum and testing regiment which allows them to master the Level II evaluations. Students successfully completing the Level II preparation will acquire the necessary math skills and confidence to progress to Liberal Studies.Level - II
Next-Generation Advanced Algebra and Functions (AAF)
assesses knowledge and skills in Linear Equations, Linear Applications and Graphs, Factoring, Quadratics, Functions, Radical and Rational Equations, Polynomial Equations, Exponential and Logarithmic Equations, and Trigonometry.
Students who aspire to follow a technical track in college will need to master the Level III College Board Assessments. Learn America’s Blended Math Accuplacer Preparatory programs will ensure better completion rates.Level - III
Studies Bound Students
Liberal Studies Bound Students
Level I Skills Pre- and Intermediate-Algebra College Mathematics
Business Studies Bound Students
Level I Skills Pre- and Intermediate-Algebra College Algebra Trigonometry, Statistics


Sudoku is a number puzzle that can strengthen logic skills. This free, printable Sudoku for Kids is available in varying degrees of difficulty. It starts at the beginner level of 4×4 grids and works progressively up to 9×9 grids. Instructions are included as well as a solution page for each set of puzzles!
Affiliate links may have been used in this post. To read our full disclaimer, click here.
Need An Affordable Approach to Learning?
Save time, money and stress with our award-winning online homeschool curriculum!


2 edition of Basic social statistics found in the catalog.
Basic social statistics
|Statement||David Knoke, George W. Bohrnstedt.|
|Contributions||Bohrnstedt, George W.|
|LC Classifications||HA29 .K735 1991|
|The Physical Object|
|Pagination||xix, 363 p. :|
|Number of Pages||363|
|LC Control Number||90063041|
Basic Statistics Covers A Wide Range Of Statistical Theory Taught In Almost All Faculties. Theory Followed By Relevant Formulae Is Fully Explicated Through Solved Numerical Problems. Mathematical Derivations And Proofs Of The Formulae Are Largely Absent. The Book Presupposes No Advance Knowledge Of veterans-opex.com Statistics Fully Covers The Syllabi Of Statistics Courses Running /5(6). Basic statistics •Statistics: “a bunch of mathematics used to summarize, analyze, and interpret a group of numbers or observations.” *It is a tool. *Cannot replace your research design, your research questions, and theory or model you want to use. 3. Population and sample.
Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences is an ideal textbook for upper-undergraduate and graduate-level research method courses in the behavioral and social sciences, statistics, and engineering. This book is also an appropriate reference for practitioners who require a review of quantitative research. Written in simple language and using easy to understand examples, Basic Statistics is an introductory statistics book that caters specially for readers taking the course for the first time.
What's a good book for learning statistics? Gotelli and Eliison's Primer of Ecological Statistics. It covers all the basic analyses, experimental design, and data management, and is approachable and easy to read. It doesn't assume you know or want to know a lot of math. level 1. 3 points · 6 years ago. Finally, it presents basic concepts in hypothesis testing. After completing this chapter, you should be familiar with the fundamental issues and terminology of data analysis, and be prepared to learn about using JMP for data analysis. Introduction: A Common Language for Researchers Research in the social sciences is a diverse topic.
method for estimating wind-wave growth and decay in shallow water with high values of bottom friction
Do the math - it is a small world.
phonology of sixteenth century American Spanish
Guide to post-school education and training.
Ten years to freedom.
Summer excursions through parts of Oxfordshire, Gloucestershire, Warwickshire, Staffordshire, Herefordshire, Derbyshire, and South Wales
The changing resource.
U.S. jobs supported by goods and services exports, 1983-94
The Uk Economy and Europe
Nutrition and disease patterns in a war affected area of eastern Nigeria.
British cinema and film statistics.
From India to America
Life and times of Lala Lajpat Rai
Algebraic Geometry (Graduate Texts in Mathematics)
Plants of the world..
Coffee stain and wrinkling to the edge of the pages when a tired undergrad fell asleep and knocked their cup over on their books. The binding and pages of the book have been reinforced with tape, has tape and stickers on the cover, as well as lots of notes (some of the answers in the learning activities may be filled in) on the veterans-opex.com: Stipes Pub Llc.
A core statistics text that emphasizes logical inquiry, not math. Basic Statistics for Social Research teaches core general statistical concepts and methods that Basic social statistics book social science majors must master to understand (and do) social research.
Its use of mathematics and theory are deliberately limited, as the authors focus on the use of concepts and tools of statistics in the analysis of social science data, Cited by: Basic Social Statistics [George Bohrnstedt] on veterans-opex.com *FREE* shipping on qualifying offers.
Bohrnstedt, GeorgeAuthor: George Bohrnstedt. Continuous variable: a variable Basic social statistics book, in theory, can take on.
all possible numerical values in a given interval. Ideally, precise intervals (distances) should be measured, as in the natural sciences. In practice, social variables usually allow only a limited number of values on a underlying continuous scale.
Jul 09, · This chapter lays out some of the basic building blocks of social statistics. First, social statistics is one of several approaches that social scientists use to link social theory to data about the world (Section ).
The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition (Springer Series in Statistics) Trevor Hastie out of 5 stars Jan 11, · Online shopping for Probability & Statistics from a great selection at Books Store. Books Advanced Search New Releases Best Sellers & More Children's Books Textbooks Textbook Rentals Sell Us Your Books Best Books of the The Basic Practice of Statistics Dec 22, by David S.
Moore and William I. Notz. Hardcover. These two books, written by statistics professors at Stanford University, the University of Washington, and the University Southern California, are the most intuitive and relevant books I’ve found on how to do statistics with modern technology.
Tibsharani is a coauthor of veterans-opex.com: Dan Kopf. data sets primarily (although not exclusively) from the social and behav-ioral areas. Although we concentrate largely on how to use SPSS to get results and on how to correctly interpret these results, the basic theoretical background of many of the techniques used is also described in separate boxes.
of economic sociology, as well as the application of social statistics to sociological data. He has written books for Oxford University Press and Cambridge UniversityAuthor: Roger Penn. Social Science Statistics.
Welcome. This web site offers free resources for students and researchers working with statistics in the social sciences. All the calculators and tools featured here have been designed with ease of use and clarity of presentation in mind.
Social statistics is the application of statistical methods to social science data. Social statistics uses the same mathematical tools as any other form of statistical analyses but it uses them in different ways that take into account the distinct features of social science data.
A core statistics text that emphasizes logical inquiry, not math Basic Statistics for Social Research teaches core general statistical concepts and methods that all social science majors must master to understand (and do) social research.
Its use of mathematics and theory are deliberately limited, as the authors focus on the use of concepts and tools of statistics in the analysis of social. To Jill Moon, graduate statistics student at George Mason University, Washington, DC, who extensively reviewed an early draft ofthe book.
To Professor William R. Benoit, Chair ofthe Business Department, Plymouth State College, Plymouth, New Hampshire, for his invaluable suggestions. Our free elementary statistics books will help you acquire a better understanding of the core concepts of statistics. The textbooks in this section cover subjects such as sampling, statistics for business and statistical analysis of social science.
Home Free textbooks for university students Statistics. Statistics. BASIC STATISTICS: FOR MEDICAL AND SOCIAL SCIENCE STUDENTS To get Basic Statistics: For Medical and Social Science Students eBook, you should follow the button below and save the document or get access to other information which are relevant to BASIC STATISTICS: FOR MEDICAL AND SOCIAL SCIENCE STUDENTS book.
Springer. Paperback. Book Condition: New. About the Book. In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time.
The Introductory Statistics teacher is no stranger to this challenge.4/4(8). Basic probability concepts An Introduction to Basic Statistics and Probability – p. 11/ Probability Mass Function f(x) - Probability mass function for a discrete random Parameters vs.
Statistics A parameter is a number that describes the population. Usually its value is unknown. Chapter 1 A Review of Basic Statistical Concepts 3 to appreciate how ingenious it was for someone to realize that writing things down solves a myriad of social and economic problems. When Basam and Gabor got into their semimonthly fistfight about whether.
Learn Basic Statistics from University of Amsterdam. Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but /5().
The course covers descriptive statistics, inference from samples, hypothesis testing, and the basics of regression analysis.
Objectives The student will become acquainted with common statistics used in the social sciences, and will learn to compute these basic statistics as appropriate for the data at hand.
Most importantly, the.i Preface This book is designed to introduce doctoral and graduate students to the process of scientific research in the social sciences, business, education, public health, and related.Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.
The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.


AP Calculus Courses
Overview of the course
There are 4 mathematics courses in the AP mathematics program. They are Pre-AP Mathematics (pre-calculus), AP Calculus AB, AP Calculus BC, and AP Statistics. Most AP centers offer Pre-calculus in year 1, Calculus AB and/or Calculus BC in year 2, and Calculus BC and/or Statistics in year 3.
The goals of the pre-calculus course are to study functions and trigonometry, prepare students for calculus, and introduce basic concepts in statistics. Both the Calculus AB and Calculus BC courses cover all topics as stated in the College Board course description for each Calculus course. Calculus AB covers the following major topic areas: analysis of functions, limits, derivatives, and integrals. Calculus BC covers all the Calculus AB topics plus infinite series and parametric, polar and vector functions.
The AP Statistics course also covers all topics as stated in the College Board course description. Major topic areas are as follows: descriptive statistics, sampling and experimentation, probability and sampling distributions, and statistical inference. In addition, planning and conducting studies is an important part of this statistics course.
Most students have a strong mathematical background from the Chinese school system, so extra emphasis is placed on vocabulary, definition of terms and the understanding of real-world applications.


Size Weight in Kgs. Gauge; in mm:Per Feet:Per Mtr. 20x20x3:0.274:0.899:25x25x3:0.335:1.099:25x25x5:0.548:1.798:31x31x3:0.390:1.280:35x35x5:0.792:2.599 Calculate Weight of a Steel Plate Chapel SteelCalculate the weight of a steel plate with Chapel's conversion calculator. Inches to Millimeters Millimeters to Inches Pounds to Kilograms Kilograms to Pounds Metric Tons to Pounds Metric Tons to Tons Fahrenheit to Celsius Celsius to Fahrenheit ft/lbs to Joules Joules to ft/lbs MPa to psi psi to MPa MPa to ksi ksi to MPa.
TMT Bar Size (In mm) TMT Bar weight in kg/m:Shyam Steel flexiSTRONG TMT Bar 5.5 mm: Calculator for Flat bars - maiak-m.bgWeight per meter:kg/m:Total weight:kg:Calculator for Flat bars Calculators. Steel sheets and plates Seamless steel pipes circular Hollow structural sections - square Hollow structural sections - rectangular Round steel bars Square steel bars Flat bars Equal angles Unequal angles Channels - GOST Channels - UPN Beams Calculator for Square steel barsmm:Length, L:m :Result Weight per meter:kg/m:Total weight:kg:Calculator for Square steel bars Calculators. Steel sheets and plates Seamless steel pipes - circular Hollow structural sections - circular Hollow structural sections
Jul 19, 2021 · If we put 1 meter length for each diameter of steel bar in the formula then we will get the unit weight. 6 mm ø bar = 6² x 1/162 = 0.222 kg/m. 8 mm ø bar = 8² x 1/162 = 0.395 kg/m. 10mm ø bar = 10² x 1/162 = 0.617 kg/m. 12mm ø bar = 12² x 1/162 = 0.888 kg/m. 16mm ø bar = 16² x Round Bar Weight Calculator - wCalculAdvanced web application can calculate material defining the round bar weight. Profile. Pipe. Round. Hexagonal. Square. MS Angle. Shears+Press Brake and Standard options available mm meters. Material. Iron. 266.393. today calculation 212. Currently 2 people doing weight calculation round bar Today was calculated weight of 212 round bars Steel Plate Weight CalculatorAug 11, 2021 · Solving for weight, we have:steel plate weight = steel plate volume * density. steel plate weight = 0.0004 m³ * 7,870 kg/m³. steel plate weight = 3.148 kilograms. However, since we need five pieces of this square steel plate, the steel plates' total weight would then be 3.148 kg * 5 = 15.74 kilograms. That's a lot of weight for just a small
Stainless Steel Bar. Stainless Steel Bar View All ; 303 Stainless Steel Bar; 304 304L Stainless Steel Bar; 316 316L Stainless Steel Bar; 321 Stainless Steel Bar; 347 Stainless Steel Bar; 410 Stainless Steel Bar; 440C Stainless Steel Bar; 13-8 mo Stainless Steel Bar; 15-5 ph Stainless Steel Bar; 17-4 Stainless Steel Bar; A286 Stainless Steel Bar Steel Weight Calculator - Steel EThe weights calculated on this steel weight calculator page are for guidance only. They are calculated using average densities for the materials. The exact composition of the material will affect the weight of the actual piece. The information provided in good faith and is for your guidance only.Calculate Weight of Steel rebar from length - 8,10,12,16 8 rows · Weight of 1 meter @ 8mm steel rod = (8 2 /162) * 1 = 0.395 kg Weight of 12 meter @ 8mm


I'm attempting to add text to a chart to show the coefficient of determination, i.e., R^2 = 0.95. Obviously, I need a superscript for this. I'm adding this using the following code:
It appears that the calculation of the position of the characters after the  is incorrect, but it's always possible that I'm doing something wrong.
Code: Select all
Chart.Canvas.TextOut(125, 140, 'R2 = 0.95', TRUE);
I'm using the newest source code version of TeeChart Pro VCL FMX 2017.22 with Delphi 10 Seattle and Firemonkey.
Can you please advise how I can fix this problem?


Happy Pi Day Everyone (3.14) Get it?
Pi Pics and Links from 2008
Here is how some math classes celebrate and don’t miss the pi song — it will hang in your brain for sure! Students participated in special PI Day activities, celebrated the day by singing PI Day songs, and (of course) the traditional eating of the pies.
Pi Day: The Other Math Holiday (pdf)
Uploaded on Mar 27, 2010 This is a music video of the song “Mathematical Pi” by Ken Ferrier and Antoni Chan.
My First Pi day post from 2011 here >>>
At 3.14 (3 minutes 14 seconds) David Letterman learns what pi means! Daniel Tammet is an amazing math genius who memorised pi to 20,000 places. Is he the world’s greatest math prodigy? He is an amazing mathematics savant or maths prodigy.
Think I’ll go have another piece of pie now just to help celebrate the day.
Posted by Sandra Crosnoe for Finding Gems & Sharing Them


There are four important properties of Indifference Curve;
Property I: Indifference curves slope downward:-
This property suggests that an indifference curve has a negative drop.
This property follows from supposition I. Indifference curve existence downward sloping means that when the amount of one good in the combination is augmented, the quantity of the other good is bargain. This must be so if the level of consummation is to remain the same on an indifference curve.
If, for example, the quantity of good X is increased in the mixture, while the quantity of good Y remains unaffected, the new combination will be better to the unique one and the two combinations will not therefore lie on the similar indifference curve provided more of a product gives more consummation.
Property II: Indifference curves are convex to the origin:-
Another significant property of indifference curves is that they are habitually convex to the origin. In additional words, the indifference curve is comparatively flatter in its rightward portion and comparatively steeper in its leftward portion. This property of indifference curves follows from assumption 3, which is that the marginal rate of substitution of X for Y reduces as more and more of X is substituted for Y.
When the indifference curve is convex to the origin, MRS reduces as more of X is replaced for K. We thus conclude that indifference curves are usually convex to the origin. Our assumption concerning diminishing MRS and the convexity of indifference curves is built upon the thought of concrete behavior of the normal customer. If indifference curves were concave or straight lines, the customer would yield to monomania, that is, he would purchase and consume only one good. We know that buyers in actual world do not usually purchase and consume one good. It is for this motive that we discard indifference curves of concave or straight-line shapes and adopt that indifference curves are usually convex to the origin.
The quantity of convexity of an indifference curve depends on the rate of decrease in the marginal rate of substitution of X for Y. As indicated above, when two goods are perfect substitutes of each other, the indifference curve is a straight line on which marginal rate of substitution remains continuous. The well substitutes the two goods are for each other, the closer the indifference curve methods to the straight line so that when the two things are perfect substitutes the indifference curve is a straight line.
Property III: Indifference curve cannot intersect each other:-
Third significant property of indifference curves is that they cannot cross each other in additional words only one indifference curve will pass over a point in the indifference map 1 his property can be simply proved by first making the two indifference curves intersect each other and then showing the irrationality or self-contradicting result it leads to.
In Fig. 8.5 two indifference curves are shown intersect each other at point C. Now take point on IC2 and point B on indifference curve IC1 steeply below A. Since indifference curve signifies those mixtures of two commodities which give equal consummation to the customer the combinations signified by points A and C will give equal satisfaction to the customer because both lie on the same indifference curve IC2.
Similarly, the mixtures B and C will give equal satisfaction to the customer; both being on the similar indifference curve IC1. If mixture A is equal to combination C in terms of satisfaction, and mixture B is equal to combination C, it follows that the mixture A will be equal to B in terms of satisfaction. But a peek at Fig.8.5 will show that this is ridiculous assumption since combination A comprises more of good Y than combination B, while the quantity of good X is the similar in both the combinations.
Therefore, the buyer will absolutely favor A to B, that is, A will give more satisfaction to the customer than B. But the two indifference curves intersect each other lead us to a ridiculous assumption of a being equal to Bin terms of satisfaction. We consequently conclude that indifference curves cannot cut each other.
Another point which is value stating in this regard is that indifference curves cannot even encounter or touch each other or be tangent to each other at a point. The gathering of two indifference curves at a point will also lead us to a ridiculous conclusion. The same quarrel holds good in this case as developed overhead in the case of connection of indifference curves.
Property IV: Higher indifference curve indicates a higher satisfaction level than a lower indifference curve:-
The last property of indifference curve is that a higher indifference curve will signify a higher level of satisfaction than a lower indifference curve. In additional words, the mixtures which lie on a higher indifference curve will be favored to the mixtures which lie on a lower indifference curve. Consider indifference curves IC1and indifference curves IC2 in Fig. 8.6. IC2 is a higher indifference curve than indifference curve IC1. Mixture Q has been taken on a higher indifference curve indifference curve IC2 and mixture S on a lower indifference curve IC1.
Mixture Q on the higher indifference curve IC2 will give a customer more satisfaction than mixture S on the lower indifference curves IC1 because the mixture Q comprises more of both goods X and Y than the mixture S. Hence the customer must favor Q to S. And by transitivity supposition, he will favor any other mixture such as mixture R on IC2 to any mixture on IC1 We, consequently, determine that a higher indifference curve signifies a higher level of satisfaction and mixtures on it will be favored to the mixtures on a lower indifference curve.
August 16, 2017


|Daisuke Takahashi and Yasumasa Kanada of the University of Tokyo computed pi to over 51 billion places of decimals. The Egyptians knew 3.16, but implicit in their Great Pyramid is the even better value 3.14. The early Hindus and Chinese were content with 3. Many ancient civilizations recognized the unique relationship between pi and circles. For example, the Babylonians approximated the value of pi as 3 (as did the Old Testament), based on the relationship between the area and radius of a circle. Thus, ancient Babylonians could celebrate an entire “Pi Month” since they assigned pi the value of 3. Later, the Greek mathematician Archimedes formulated a geometrical algorithm to estimate pi by comparing the perimeters of polygons and circles. The Romans rolled all over the world in chariots whose wheels they believed to be exactly 3.125 times as far around as they were across. In the 1690s, Isaac Newton and Gottfried Leibniz bridged the gap between algebra and geometry and used calculus to figure out pi’s first 15 digits. The 20th century athematician Srinivasa Ramanujan used even more powerful tools like number theory and elliptic integrals to find new ways to compute pi further.
Pi, an abstract notion, is defined as the ratio between the circumference and the diameter of a circle. It’s an irrational number that cannot be expressed as a fraction and runs into infinity and is generally rounded up at 3.14. Every year on 14th March International Pi Day is celebrated, but this year is particularly special, one that occurs once in a century. On 3/14/15 at 9.26 and 53 seconds, the date and time spelled the first 10 digits of pi. The National Institutes of Health (NIH) celebrated the intersection between the quantitative and biomedical sciences that included lectures as well as brainstorming mathematical problems that can be applied to real-world situations.


Joel E. E. Cohen, Rockefeller University and Columbia University
Stewart (1947) and Clark (1951) proposed that urban population density is a negative exponential function of the distance from a city's center. This model has been influential in urban economics, transportation planning, and urban demography. Duncan (1957) suggested characterizing the inequality in the distribution of urban population density in this model by using standard economic measures of concentration or unevenness: the Lorenz curve, the Gini coefficient, and the Hoover dissimilarity index. Batty (1974) advocated measuring concentration using relative entropy. We execute their suggestions using mathematical analysis, not simulations. We modify the negative exponential model to recognize that any city has a finite radius. Mathematical analysis reveals that all four measures of concentration depend sensitively on the boundary radius in the negative exponential model. We give a numerical example of the sensitivity of the concentration measures to the boundary radius. In empirical applications of the negative exponential model of urban population density, it is important to have consistent standards for defining urban boundaries. Otherwise, differences between cities or over time within the same city in these and perhaps other measures of concentration could be due at least in part to differences in defining the radius or other boundaries of the city.
Keywords: Urbanization and urban populations, Mathematical demography, Spatial dependence/heterogeneity, Population geography
Presented in Session 83. Data and Methods: A Medley of Perspectives