Common

Eisenstein integer

Complex number whose mapping on a coordinate plane produces a triangular lattice

Eisenstein integer

Common card · No. 404700

In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form z=a+bω, where a and b are integers and ω=−1+i32=ei2π/3 is a primitive (hence non-real) cube root of unity. The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex plane. The Eisenstein integers are a countably infinite set.

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