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INTEGER POLYGONS OF GIVEN PERIMETER

Published online by Cambridge University Press:  30 January 2019

JAMES EAST
Affiliation:
Centre for Research in Mathematics, Western Sydney University, Sydney, Australia email J.East@WesternSydney.edu.au
RON NILES
Affiliation:
Memverge Inc., San Jose, California 95134, USA email rniles@yahoo.com
Corresponding

Abstract

A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter $n$ is the nearest integer to $n^{2}/48$ ($n$ even) or $(n+3)^{2}/48$ ($n$ odd). We solve the analogous problem for $m$-gons (for arbitrary but fixed $m\geq 3$) and for polygons (with arbitrary number of sides).

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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References

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