Fun definition of pi. If ever the definition wasn’t much fun !
One of the very best in Mathematics I have seen. Must watch.
Get Geeky today :)
(Visualization of a higher dimensional object)The tesseract is a four dimensional cube. It has 16 edge points v=(a,b,c,d), with a,b,c,d either equal to +1 or -1. Two points are connected, if their distance is 2. Given a projection P(x,y,z,w)=(x,y,z) from four dimensional space to three dimensional space, we can visualize the cube as an object in familar space. The effect of a linear transformation like a rotation
| 1 0 0 0 | R(t) = | 0 1 0 0 | | 0 0 cos(t) sin(t) | | 0 0 -sin(t) cos(t) |
in 4d space can be visualized in 3D by viewing the points v(t) = P R(t) v in R3.