World 2 · Nets & Folding · 8 minEuler's formula
F − E + V = 2
Teaching this? Open projector mode
Count faces, edges and vertices of any solid with flat faces and no holes, then work out F − E + V. You always get 2.
- Cube: 6 − 12 + 8 = 2
- Square pyramid: 5 − 8 + 5 = 2
- Tetrahedron: 4 − 6 + 4 = 2
Leonhard Euler wrote this down in 1750. It is one of the first results of topology, the maths of shape without measurement.
Check yourself
A prism has a 7-sided base. How many edges does it have?
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