Integer triangles of given perimeter : a new approach via group theory

James East; Ron Niles

doi:10.1080/00029890.2019.1632632

Integer triangles of given perimeter : a new approach via group theory

James East, Ron Niles

Western Sydney University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The following question has been considered by several mathematicians over the last half century: How many incongruent triangles with integer sides have perimeter n? We present a new solution based on group actions and orbit enumeration.

Original language	English
Pages (from-to)	735-739
Number of pages	5
Journal	American Mathematical Monthly
Volume	126
Issue number	8
DOIs	https://doi.org/10.1080/00029890.2019.1632632
Publication status	Published - 2019

Keywords

group theory
incongruity
integer programming
triangle

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10.1080/00029890.2019.1632632

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title = "Integer triangles of given perimeter : a new approach via group theory",

abstract = "The following question has been considered by several mathematicians over the last half century: How many incongruent triangles with integer sides have perimeter n? We present a new solution based on group actions and orbit enumeration.",

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AU - Niles, Ron

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AB - The following question has been considered by several mathematicians over the last half century: How many incongruent triangles with integer sides have perimeter n? We present a new solution based on group actions and orbit enumeration.

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KW - incongruity

KW - integer programming

KW - triangle

UR - https://hdl.handle.net/1959.7/uws:54178

U2 - 10.1080/00029890.2019.1632632

DO - 10.1080/00029890.2019.1632632

M3 - Article

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VL - 126

SP - 735

EP - 739

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 8

ER -

Integer triangles of given perimeter : a new approach via group theory

Abstract

Keywords

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