A primitive right triangle is a right triangle having integer sides , , and such that , where is the greatest
common divisor . The set of values is then known as a primitive
Pythagorean triple .
The smallest known area shared by three primitive right triangles is 13123110, corresponding to the triples (4485, 5852, 7373), (1380, 19019,
19069), and (3059, 8580, 9109) (Beiler 1966, p. 127; Gardner 1984, p. 160),
as discovered by C. L. Shedd in 1945.
See also Primitive Pythagorean Triple ,
Pythagorean Triangle ,
Pythagorean
Triple ,
Right Triangle
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References Beiler, A. H. "The Eternal Triangle." Ch. 14 in Recreations
in the Theory of Numbers: The Queen of Mathematics Entertains. New York:
Dover, 1966. Gardner, M. The
Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University
of Chicago Press, pp. 160-161, 1984. Referenced on Wolfram|Alpha Primitive Right Triangle
Cite this as:
Weisstein, Eric W. "Primitive Right Triangle."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/PrimitiveRightTriangle.html
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