Euler: V- E + R = 2

1. Euler wrote to Goldbach @1750, "it astonishes me these properties have not been noticed by anyone else."

Euler's Polyhedron formula:

V- E + R = 2

Remember trick: “VERsion 2”
V= Vertices, E= Edges, R= Regions (or Faces)
Note: = 0 (instead of 2) for torus doughnut

2. Euler proved it 1 year later: intuition leads to discovery, then prove it by logic.

Example:
Football: Vertices=60, Edges E=90, Region R=32 faces (12 pentagons, 20 hexagons):
V- E + R = 60 - 90 + 32 = 2

[caption id="" align="alignright" width="300"] A football (or soccer ball) icon. (Photo credit: Wikipedia)[/caption]