Category:Euler's Theorems

This category contains pages concerning Euler's Theorem:

Euler's Theorem (Number Theory)

Let $a, m \in \Z$ be coprime integers: $a \perp m$.

Let $\map \phi m$ be the Euler $\phi$ function of $m$.

Then:

$a^{\map \phi m} \equiv 1 \pmod m$

Euler Theorem on Curvature of Surface

Let $S$ be a surface in space.

The principal directions of the curvature of $S$ are perpendicular to each other.

Euler's Theorem for Planar Graphs

Let $G = \struct {V, E}$ be a connected planar graph with $V$ vertices and $E$ edges.

Let $F$ be the number of faces of $G$.

Then:

$V - E + F = 2$

Euler's Theorem for Polyhedra

For any convex polyhedron with $V$ vertices, $E$ edges, and $F$ faces:

$V - E + F = 2$

Source of Name

This entry was named for Leonhard Paul Euler.