How to generate all integral triangles containing a given angle
We present an elementary prescription based on the rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization of the ancient problem of finding all the Pythagorean triples. As an example, we discuss a specific equati...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117120000048X |
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| Summary: | We present an elementary prescription based on the
rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization
of the ancient problem of finding all the Pythagorean triples. As
an example, we discuss a specific equation studied by Diophantus of
Alexandria, which turns out to be equivalent to the problem of
finding all the integral triangles containing a
60∘ angle. The material developed here is elementary
enough for inclusion in undergraduate courses and advanced high
school courses. |
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| ISSN: | 0161-1712 1687-0425 |