1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle. But what if, instead of the circle, we used a regular polygon? In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1. (There’s a very neat reason for this.) Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon. More on this subject and derivations of the functions can be found in this other post

Now you can also listen to what these waves sound like

This technique is general for any polar curve. Here’s a heart’s sine function, for instance

wired:

Beautiful, ominous, and surprising, these are the winners of the 2012 International Science and Engineering Visualization Challenge. For 10 years, the competition — sponsored by the National Science Foundation and the journal Science — has celebrated the creators of visually striking, informative, and original art. The 2012 winners were just announced. From glowing corals to spiky seeds to neural networks on a chip, these images speak more clearly — and louder — than any report ever could.

See the rest of the winners over @ Wired Science.