Euler polyhedron formula
Fórmula de Euler para poliedros (V - A + C = 2)
- Date
- 1750 · confidence high
- Place
- Berlin, Prussia
- Credited to
- Leonhard Euler; unpublished earlier work by Descartes (c. 1630)
- People
- 👤 Leonhard Euler1707–1783
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
For every convex polyhedron, vertices minus edges plus faces equals two. The first topological invariant, independent of lengths and angles.
Euler's proof had gaps; Legendre (1794) and Cauchy (1811) completed it, and Lakatos used it as a case study in Proofs and Refutations.
What it led to
- the Euler characteristic
- algebraic topology
- the classification of surfaces
- the four colour theorem (planarity)