Current location - Training Enrollment Network - Mathematics courses - Number of discrete mathematical surfaces
Number of discrete mathematical surfaces
1.V=6, E= 12, connected simple plane, Euler characteristic F-E+V = 2 = = "F = 8.

Let F=a3+a4+...+an, where ai is the number of faces with degree i. therefore

a3+a4+...+an=8

2E=3a3+4a4+..+ Male

Namely:

24=3a3+4a4+..+ Male

8 = A3+4/3A4+...+N/3A

0 = 8-(a3+a4+...+an) =1/3a4+...+n/3an.

Because ai>= 0, I = 3, ..., N., there must be a4=...=an=0, so a3=8.

In other words, there are eight faces with the number 3.

2. 1400= 2^3*5^2*7

Therefore, the number of positive factors of 1400 is: (3+1) * (2+1) * (1+1) = 24.