Euler Characteristic Index

According to Euler Characteristic Index Theorem V-E+F=0, we can conclude that there are exactly 5 Platonic solids.The index of sphere(S2) is 2, and the index of torus is 0.

Delaunay Triangulation

Delaunay triangulation is the dual graph of Vonoroi graph, it is important in computational geometry.


In this note, we introduce the difinition of simplex( convex combinition of vertices), we find Pascal triangle in n-simplex, it is interesting.

Volume of n-ball

The volume of n dimensional ball is interesting, for fixed radius, when n is 5, the volume is maximum, when n approaches to infinity, the volume approaches to zero.