Maths
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A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring . Let the sphere have radius and the cylinder radius . Note that as illustrated above, the hole cut out consists of a cylindrical portion plus two spherical caps .
Spherical Ring -- from Wolfram MathWorld
Ring turns into a sphere - Boing Boing
This replica of a 17th century gold armillary ring swings open to form a sphere; the original came from Diana Scarisbrick's Historic Rings . This one (which improves on the original) was made by LiveJournaller Acanthusleaf. Link ( Thanks, Monique! ) Share this post
The binomial theorem expands powers of sums. The binomial coefficient is the number of ways to choose k objects from a set of n objects, regardless of order. The golden ratio, phi.
Math Gems
In probability and statistics , Student’s t -distribution (or simply the t -distribution ) is a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It plays a role in a number of widely-used statistical analyses, including the Student’s t -test for assessing the statistical significance of the difference between two sample means , the construction of confidence intervals for the difference between two population means, and in linear regression analysis . The Student’s t -distribution also arises in the Bayesian analysis of data from a normal family. The t -distribution is symmetric and bell-shaped, like the normal distribution , but has heavier tails, meaning that it is more prone to producing values that fall far from its mean.
Student's t-distribution
math Symbols
\sqrt{x} Relations Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word.
This algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples.
Math Help
Maths is flawed because of Zero
so your third step also involves dividing by zero which isn’t allowed! Instead, we can think about the function and see what happens as x>0 gets small. We have: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . The variable x having a value close to zero is different than it having a value of exactly zero. It turns out that is undefined. does not have a value.
Weierstrass functions
It is not hard to show that this series converges for all x . In fact, it is absolutely convergent . It is also an example of a fourier series , a very important and fun type of series. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x . You can see it's pretty bumpy.
Education
Maths - team curated
Mathematical Background
by John F. Sowa This web page is a revised and extended version of Appendix A from the book Conceptual Structures by John F. Sowa. It presents a brief summary of the following topics for students and general readers of that book and related books such as Knowledge Representation and books on logic, linguistics, and computer science. Note: Special symbols in this file that are outside the Latin-1 character set (ISO 8859-1) are represented by a .gif image for each character.Get in touch to tell us where you're listening from and what's happening in your world, or with any questions, comments or puzzles, at samuel@acmescience.com
Math/Maths 50: 1st Birthday Spectacular! | Pulse-Project.org
Mathematical Works
Maths Software
Bezier curves - a primer
So, with that out of the way, let's look at the topic at hand: Bézier curves. In order to draw things in 2D, we rely on two kinds of drawing primitives: the straight line, and the curved line. While we can draw loads of things freehand, computers are a bit handicapped in that drawing straight lines is dead-easy for them, but they can't draw curves unless there is a mathematical function that describes how it should be drawn.slehar@cns.bu.edu Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery. Fourier theory states that any signal, in our case visual images, can be expressed as a sum of a series of sinusoids.
An Intuitive Explanation of Fourier Theory
Instead I am concentrating recommendations and examples within the undergraduate mathematics curriculum, so please visit the Open Math Curriculum page. If you are linking to this site, please use that page for a broad list, or link to linear.pugetsound.edu specifically for the Linear Algebra text. Thanks for your help publicizing open textbooks. This page contains some links to similar open-source textbooks. Notice however that a book that is free to download, but with a copyright that reserves the author's rights, is not really free.