Euler's identity

In mathematical analysis, Euler's identity, named after Leonhard Euler, is the equation where Euler's identity is also sometimes called Euler's equation. Euler's identity is considered by many to be remarkable for its mathematical beauty. Three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: Furthermore, in mathematical analysis, eq... more

In mathematical analysis, Euler's identity, named after Leonhard Euler, is the equation where Euler's identity is also sometimes called Euler's equation. Euler's identity is considered by many to be remarkable for its mathematical beauty. Three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: Furthermore, in mathematical analysis, equations are commonly written with zero on one side. A reader poll conducted by Mathematical Intelligencer named the identity as the most beautiful theorem in mathematics. Another reader poll conducted by Physics World in 2004 named Euler's identity the "greatest equation ever", together with Maxwell's equations. The book Dr. Euler's Fabulous Formula [2006], by Paul Nahin (Professor Emeritus at the University of New Hampshire), is devoted to Euler's identity; it is 400 pages long. The book states that the identity sets "the gold standard for... less