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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.
A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6]
Euler brick; Euler's constant; F. Feit–Thompson conjecture; Fermat number; Fermat–Catalan conjecture; Fibonacci prime; Firoozbakht's conjecture; Four exponentials ...
Euler brick; Euler's line – relation between triangle centers; Euler operator – set of functions to create polygon meshes; Euler filter; Euler's rotation theorem; Euler spiral – a curve whose curvature varies linearly with its arc length; Euler squares, usually called Graeco-Latin squares
Eugene Catalan Prize-- Eugene Chan-- Euler angles-- Euler Book Prize-- Euler–Boole summation-- Euler brick-- Euler calculus-- Euler characteristic-- Euler characteristic of an orbifold-- Euler class-- Euler diagram-- Euler equations-- Euler equations (fluid dynamics)-- Euler filter-- Euler function-- Euler integral-- Euler integral ...
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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
This equation, stated by Euler in 1758, [2] is known as Euler's polyhedron formula. [3] It corresponds to the Euler characteristic of the sphere (i.e. = ), and applies identically to spherical polyhedra. An illustration of the formula on all Platonic polyhedra is given below.