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Euler brick

In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.

Perfect cuboid, Connection to elliptic curves & Generating formula

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Overview

Definition

Properties

Examples

Generating formula

Perfect cuboid

Almost-perfect cuboids

Perfect parallelepiped

Connection to elliptic curves

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Map overview Semantic statistics

Euler brick

Nodes45
Edges44
Triples24
Avg. degree1.96
Density0.044444
Components1

How this topic connects Entity context

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Euler brick

Top relations

related to Generating formula · 6
Euler brick → An, Euler, Let, Pythagorean, Saunderson's, Then
related to Perfect cuboid · 5
Euler brick → As, Diophantine, Euler, In, March
related to Properties · 5
Euler brick → Consequently, Euler, Exactly, Given, If
related to Examples · 4
Euler brick → Euler, Paul Halcke, Some, The
related to Definition · 3
Euler brick → Diophantine, Euler, The
is a · 1
Euler brick → Euler brick whose edge lengths are relatively prime

Important terminology Word statistics

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Important terminology

cuboid perfect face euler edge integer one diagonal space brick edges cuboids divisible must diagonals two lengths also heronian length

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Euler brickis aEuler brick whose edge lengths are relatively prime0.90text
Euler brickrelated to DefinitionThe0.60section
Euler brickrelated to DefinitionEuler0.60section
Euler brickrelated to DefinitionDiophantine0.60section
Euler brickrelated to ExamplesThe0.60section
Euler brickrelated to ExamplesEuler0.60section
Euler brickrelated to ExamplesPaul Halcke0.60section
Euler brickrelated to ExamplesSome0.60section
Euler brickrelated to Generating formulaEuler0.60section
Euler brickrelated to Generating formulaAn0.60section
Euler brickrelated to Generating formulaSaunderson's0.60section
Euler brickrelated to Generating formulaLet0.60section

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    Min side: 3
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