Boy, Oh Boy

Firstly, today I must apologize for the lack of posts yesterday. The pre-publish system didn’t work as I hoped, but I got that sorted out anyways.

Today’s Math-Art is a Boy’s Surface. A Boy’s Surface is a plane, immersed in 3D Space. And because it twists in 3D-space, it does self-intersect. If it sounds all complicated, don’t worry, I personally don’t get much of it too. I suppose a helpful way would be to think of Klein bottles, and instead of 3D-objects in a 4D space, think of a 2D object immersed in a 3D space.

This Boy’s Surface was rendered by Adam Coffman, a professor in geometry in Purdue University, Fort Wayne. And the formula of which he gave was this:

t=1: 36zy⁴ + 36x²z⁴ + 36x⁴z - 243x⁴y² - 243x²y⁴ + 36z⁴y² + 72x²zy² - 48sz³y³ + 72sy²z³x - 90y⁴z² - 16y²z² - 16z²x² - 90z²x⁴ - 81y⁶ - 24z⁶ + 48z⁵ - 32z⁴ + 64z³/9 - 81x⁶ - 180y²z²x² - 24sz³x³ + 48sy³z² - 144syz²x² - 324sy⁴zx - 216sy²zx³ + 108szx⁵ + 144sx²z³y = 0

I chose this picture because despite its complexity (well, to a math PhD, it’s not really that complex), it still exhibits a simplistic image. And the picture remind me of Apple Mac ads too.