Eisenstein Integer

(Systolic Geometry)

Logo of Eisenstein integer
sciences
Systolic Geometry
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What is Eisenstein integer?

In mathematics, Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are complex numbers of the form where a and b are integers and 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.

Technology Types

algebraic numberamountcomplex numbercyclotomic fielddefinite quantityirrational numberlattice pointmagnitudequadratic irrational numberreal numbersystolic geometry

Synonyms

Eisenstein-Jacobi integerEuler integerEuler integersEulerian integerEulerian integers

Translations

Eisenstein-Zahl (de)Eisensteinovo číslo (cs)Enter d'Eisenstein (ca)Entero de Eisenstein (es)Entier d'Eisenstein (fr)Geheel getal van Eisenstein (nl)Inteiro de Eisenstein (pt)Intero di Eisenstein (it)Liczby całkowite Eisensteina (pl)Ціле число Ейзенштейна (uk)Число Эйзенштейна (ru)عدد أيزنشتاين الصحيح (ar)아이젠슈타인 정수 (ko)アイゼンシュタイン整数 (ja)艾森斯坦整数 (zh)

Tech Info


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