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![reb36g:
This animation suggests one way to draw a perfect ellipse by hand. Place two drawing pins in a board, and tie a piece of string around them (the red dotted lines in the picture). If you pull the string tight with a pen, then the curve you will get is an ellipse. This means that the total length of the two red lines is constant. The two pins are at the foci of the ellipse, special points. Planetary orbits are ellipses, with the Sun at a focus. What would happen if you moved the pins closer and closer to each other? [code] [more]](http://24.media.tumblr.com/tumblr_llvm3lHgYA1qfg7o3o1_250.gif)
![reb36g:
Is it possible to find a pattern in the prime numbers? If you arrange them in what is called the Ulam spiral, you can see some clear patterns emerging. There are other spiral shapes which give nice patterns, such as stacking them into a triangle. Here I have tried wrapping them into a Fibonacci spiral, where each dot is slightly further out than the last- and is rotated by a Golden ratio of a full turn (about 0.618034 * 360 = 222.49224 degrees). The red dots are the primes, the blacks the non-primes (composites). Unfortunately, there doesn’t seem to be any pattern. Does there? [code]](http://24.media.tumblr.com/tumblr_lp3nr3qkFi1qfg7o3o1_250.gif)
