Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-04-30T15:38:59.665Z Has data issue: false hasContentIssue false
  • English
  • Français

Less than equable Heronian triangles

Published online by Cambridge University Press:  17 October 2016

Stan Dolan
Stan Dolan*
Affiliation:
126A Harpenden Road, St Albans AL3 6BZ
Get access Rights & Permissions [Opens in a new window]

Extract

It is well known that there are precisely five integer-sided triangles which have equal area, Δ, and perimeter, P. These triangles are called equable Heronian triangles.

A proof of this result was given by Whitworth [1]. Since Whitworth's time, much attention has been given to triangles whose areas are integer multiples of their perimeters, for example [2, 3]. However, as this paper will show, Heronian triangles with areas less than their perimeters have some mathematical interest.

Type
Articles
Information
The Mathematical Gazette , Volume 100 , Issue 549 , November 2016 , pp. 482 - 489
Copyright
Copyright © Mathematical Association 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Whitworth, W. A., Mathematical questions from the Educational Times, 5 (1904) pp. 62–63.Google Scholar
2. Crilly, T. and Fletcher, C. R., The ‘hitchhiker triangle’ and the problem of perimeter = area, Math. Gaz. 99 (November 2015) pp. 402–415.Google Scholar
3. Markov, L., Heronian triangles whose areas are integer multiples of their perimeters, Forum Geometricorum, 7 (2007) pp. 129–135.Google Scholar
4. Dukić, Dusšan, Pell's Equations, Olympiad training materials, accessed June 2016 at http://imomath.com./ Google Scholar