Euler's formula

noun

1. Mathematics.,  the theorem that e ix = cos x + i sin x.

2. Mechanics.,  a formula for determining the maximum load that can be applied to a given column without causing it to buckle.

Word History and Origins

Origin of Euler's formula¹

First recorded in 1945–50; named after L. Euler

Example Sentences

One of the designers, Zita Hsu, explains that they found inspiration in a mathematical concept known as Euler’s formula to create an abstract design.

Read more on Economist

Other winners of the equation beauty contest included the Pythagorean identity, the identity between exponential and trigonometric functions derivable from Euler’s formula for complex analysis, and the Cauchy-Riemann equations.

Read more on Scientific American

Athreya recalls that some of the student groups noticed the pattern that v – e + f = 2 for convex polyhedra, a nontrivial fact known as Euler's formula.

Read more on Scientific American

Marco M jumped in at the end with a bit of Euler’s formula — something I’m sure we’ll explore in a future post.

Read more on New York Times