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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

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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.

Information

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

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