The Euler formula, sometimes also called the Euler identity, states
where is the imaginary unit. Note that Euler’s polyhedral formula is sometimes also called the Euler formula, as is the Euler curvature formula.
The special case of the formula with gives the beautiful identity
an equation connecting the fundamental numbers and , 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.