Nature by numbers. The theory behind this movie
We can find interactive sites on the internet (like this) to draw points, move them, and check how the structure becomes updated in real time. In fact, if we have a series of random dots scattered in the plane, the best way of finding the correct Voronoi Telesación for this set is using the Delaunay triangulation. And in fact, this is precisely the idea shown on the animation: first the Delaunay Triangulation and then, subsequently, the Voronoi Tessellation. But to draw a correct Delaunay Triangulation is necessary to meet the so-called “Delaunay Condition”.
Triangle Dissection Paradox
The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area one unit larger than the top figure (as indicated by the grid square containing the dot). The source of this apparent paradox is that the "hypotenuse" of the overall "triangle" is not a straight line, but consists of two broken segments.

Blog : Twisted Architecture
I didn’t set out to tie knots in Norman Foster’s Hearst Tower or wrinkle his Gherkin, but I got carried away. It’s one of the occupational hazards of working with Mathematica. It started with an innocent experiment in lofting, a technique also known as “skinning” that originated in boat-building.
cgi-bin Matrix Solver
Solving a linear equation system of up to 20 unknowns. If you need some help please scroll down to the example. If not, fill the 2 boxes below , then click on the "Go" button. Example As an example, let's say you have the following 3 equations to solve for the unknowns x , y , and z : 2x + 3y + 1/3z = 10 3x + 4y + 1z = 17 2y + 7z = 46

11 cheap gifts guaranteed to impress science geeks
Science comes up with a lot of awesome stuff, and you don't need a Ph.D, a secret lab, or government funding to get your hands on some of the coolest discoveries. We've got a list of 11 mostly affordable gifts that are guaranteed to blow your mind, whether or not you're a science geek. Click on any image to see it enlarged. 1.
The Thirty Greatest Mathematicians
Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list.

Mathematical Atlas: A gateway to Mathematics
Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions.
Banach-Tarski Paradox
Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original? This theorem is known as the Banach-Tarski paradox. So why can't you do this in real life, say, with a block of gold? If matter were infinitely divisible (which it is not) then it might be possible. But the pieces involved are so "jagged" and exotic that they do not have a well-defined notion of volume, or measure, associated to them. In fact, what the Banach-Tarski paradox shows is that no matter how you try to define "volume" so that it corresponds with our usual definition for nice sets, there will always be "bad" sets for which it is impossible to define a "volume"!