math
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I feel like talking about some pure math, just for fun on a Sunday afternooon. Back in 2006, Dan Christensen did something rather simple and got a surprisingly complex and interesting result. He took a whole bunch of polynomials with integer coefficients and drew their roots as points on the complex plane.
The Beauty of Roots « Azimuth
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delaunay
www.iki.fi/sol - Tutorials - Interpolation Tricks
While making demos I've found different interpolation tricks to be extremely valuable. Adding little smoothness to all kinds of movement, be it actual movement of the camera, some object, fading of lights, fading in and out etc, makes things much more enjoyable to watch. Sharp movements and changes are jarring and should be avoided. (*1) Generally speaking, when making some kind of animation, we know the starting and ending positions, and want to transition between these.A set V consists of n elements if its elements can be counted 1, 2,..., n . In other words, the set V can be brought into a 1-1 correspondence with the set Often it's more convenient to start counting from 0. Then we get the set A permutation is a 1-1 correspondence of a set V onto itself: Being able to count elements in the set V means the set can be written as However, a set may be counted in many different ways.
Permutations
College Algebra Tutorial on The Fundamental Counting Principle
In general there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The first digit is limited to being the number 5, so there is only one possibility for that one. There are no restriction on digits 2 - 4, so each one of those has 10 possibilities. In general, there are 26 letters in the alphabet. The first letter, cannot be a vowel (a, e, i, o, u), so that means there are 21 possible letters that could go there. The second letter has no restriction, so there are 26 possibilities for that one.
If you have a graphing calculator, it will be hidden under the MATH menu screen and then select your Probability screen - there you should find !
College Algebra Tutorial on Permutations