Euler's formula
Links exponentials, trigonometry
Euler's formula is the mathematical identity e^(iπ) + 1 = 0, which unites five fundamental constants—e, i, π, 1, and 0—in a single equation.
More generally, Euler's formula states that e^(ix) = cos(x) + i·sin(x), linking exponential and trigonometric functions through complex numbers.
The special case where x = π yields the celebrated identity.
Mathematicians often call it the most beautiful equation in mathematics.
- exponential functionOutput multiplies by fixed ratio
- cosineRatio in triangle math
- imaginary numbersMultiples of i
- tetrahedronFour-faced polyhedron
- verticesCorner points of shapes
unit circle · edges · mathematics · radians · polyhedra · faces · complex plane · polar coordinates · cube · topology · symmetry · mathematical constants · transcendental · beautiful · geometry · pi · angle · oscillation
Euler's formulaFermat's Last Theorem
No integer cubes sum to cubes
axiom · postulate · Pythagorean theorem · empirical observation · self-evident truth
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