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A Condition for Right-Angled Triangles

Published online by Cambridge University Press:  03 November 2016

B. D. Price
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Extract

IT is well known that the identity

enables one to generate right-angled triangles with integral sides merely by putting x and y as integers (x>y). It is sufficient that x, y be integers, to give a right-angled triangle with hypotenuse x2+y2 and sides x2—y2, 2xy. Is the condition necessary? No, for the triangle with sides 9, 12, 15 (a multiple of the 3, 4, 5 case) cannot be expressed by the above identity without using surds. VVe will, however, prove the following proposition:

Type
Research Article
Information
The Mathematical Gazette , Volume 33 , Issue 304 , May 1949 , pp. 121 - 122
Copyright
Copyright © Mathematical Association 1949

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