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Heron triangles with two fixed sides |
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| Authors: | Eugen J Ionascu |
| Institution: | a Columbus State University, 4225 University Avenue, Columbus, GA 31907, USA b Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, Mexico c Naval Postgraduate School, Applied Mathematics Department, Monterey, CA 93943, USA |
| Abstract: | In this paper, we study the function H(a,b), which associates to every pair of positive integers a and b the number of positive integers c such that the triangle of sides a, b and c is Heron, i.e., it has integral area. In particular, we prove that H(p,q)?5 if p and q are primes, and that H(a,b)=0 for a random choice of positive integers a and b. |
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