Euler's theorem (idea) by krimson

Probably the most stupid name you could give a theorem. Leonhard Euler was a an extremely productive mathematician who made contributions to practically all fields of mathematics. The result is that there is not just one Euler's theorem, but lots and lots. After a while people started naming theorems after the next guy to investigate it after Euler had discovered it.

Some examples:

Euler's theorem (number theory):
If a and n are coprime then a^φ(n) ≡ 1 (mod n). (Discussed in detail below by Noether.)

Euler's theorem (vector calculus):
f : Rⁿ → R is homogeneous function of degree n iff (x.∇)f = nf.

Euler's theorem (kinematics):
For any rigid body rotation there is an instantaneous axis of rotation (ie. a straight line of points instantenously at rest).

The long list of mathematical concepts named after Euler also includes items such as the Euler characteristic, the Euler formula, the Euler line, Euler's constant, the Euler momentum equation and the Euler-Lagrange equations.

Euler formula	Fermat's little theorem	Euler Phi function	integers modulo n
coprime	Leonhard Euler	Euler's identity	Lagrange's Theorem
Euler	Dimensionless Numbers	Euler's constant	Euler characteristic
Congruent	theorem	RSA	Lemma of Choice
March 5, 2004	Euler Product Formula	Euler line	de Moivre's formula
Mathematics of RSA	multiplicative group	Four color theorem