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On HAP triangles
Published online by Cambridge University Press: 20 June 2025
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It is a well known and easily verifiable fact that not all integer triangles have integer areas. Consider the triangles with sides {9, 10, 17}, {13, 14, 15}, {5, 7, 8} and {6, 7, 9} with respective areas 36, 84, 
and 
. The first two, whose areas are integers, are called Heronian triangles. The second triangle also has the additional property that its sides are consecutive integers and is an example of a Brahmagupta triangle, named after an Indian mathematician, born in AD 598. These are called Super-Heronian triangles in [1] and a method is developed there for generating examples of such triangles.
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- © The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association
References
Richardson, William H., Super-Heronian triangles (2010), available at https://www.math.wichita.edu/~richardson/heronian/heronian.html
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