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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. Euler brick with edges a , b , c and face diagonals d , e , f
Pages in category "Arithmetic problems of solid geometry" ... Euler brick; H. Heronian tetrahedron This page was last edited on 3 April 2023, at 01:22 (UTC). ...
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]
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A Pythagorean quadruple is called primitive if the greatest common divisor of its entries is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. The set of primitive Pythagorean quadruples for which a is odd can be generated by the formulas = +, = (+), = (), = + + +, where m, n, p, q are non-negative integers with greatest common divisor 1 such that m + n + p + q is o
In mathematics, Harborth's conjecture states that every planar graph has a planar drawing in which every edge is a straight segment of integer length. [1] [2] [3] This conjecture is named after Heiko Harborth, and (if true) would strengthen Fáry's theorem on the existence of straight-line drawings for every planar graph.
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.
Euler's proof of the zeta product formula contains a version of the sieve of Eratosthenes in which each composite number is eliminated exactly once. [9] The same sieve was rediscovered and observed to take linear time by Gries & Misra (1978). [19] It, too, starts with a list of numbers from 2 to n in order. On each step the first element is ...