This is a (subset of the) list of the most beautiful math equations ever derived, according to Ed Pegg Jr and Eric Weisstein (Mathworld). You can check the whole list here.

**Archimedes’ Recurrence Formula**

Let and be the perimeters of the circumscribed and inscribed *n*-gon and and the perimeters of the circumscribed and inscribed *2n*-gon. Then

Successive application gives the Archimedes algorithm, which can be used to provide successive approximations to .

**Euler Formula**

This equation connects the fundamental numbers *i*, , *e*, 1, and 0, the fundamental operations , , and exponentiation, the most important relation , and nothing else. Gauss is reported to have commented that if this formula was not immediately obvious, the reader would never be a first-class mathematician.

**Euler-Mascheroni Constant**

The Euler-Mascheroni constant gamma, sometimes also called `Euler’s constant’ or `the Euler constant’, is defined as the limit of the sequence

has the numerical value 0.577215664901532860606512090082402431042…

**Riemann Hypothesis**

The Riemann hypothesis is a deep mathematical conjecture which states that the non-trivial Riemann zeta function zeros, i.e., the values of *s* other than -2, -4, -6, such that (where is the Riemann zeta function) all lie on the “critical line” (where denotes the real part of *s*).

The Riemann zeta-function is the function of a complex variable s initially defined by the following infinite series:

The Riemann hypothesis can be stated as:

and implies .

**Gaussian Integral**

The Gaussian integral, also called the probability integral is the integral of the one-dimensional Gaussian function over

http://mathoverflow.net/questions/3134/whats-your-favorite-equation-formula-identity-or-inequality/5680#5680