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# Rational Triangle

Somos defines a rational triangle as a triangle such that all three sides measured relative to each other are rational. Koblitz (1993) defined a congruent number as an integer that is equal to the area of a rational right triangle. The discovery that a right triangle of unit leg length has an irrational hypotenuse (having a length equal to a value now known as Pythagoras's constant) showed that not all triangles are rational.

Conway and Guy (1996) define a rational triangle as a triangle all of whose sides are rational numbers and all of whose angles are rational numbers of degrees. The only such triangle is the equilateral triangle (Conway and Guy 1996).

Congruent Number, Equilateral Triangle, Fermat's Right Triangle Theorem, Heronian Triangle, Pythagoras's Constant, Rational Quadrilateral, Right Triangle

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## References

Conway, J. H. and Guy, R. K. "The Only Rational Triangle." In The Book of Numbers. New York: Springer-Verlag, pp. 201 and 228-239, 1996.Koblitz, N. Introduction to Elliptic Curves and Modular Forms. New York: Springer-Verlag, 1993.Somos, M. "Rational Triangles." http://grail.csuohio.edu/~somos/rattri.html.

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Rational Triangle

## Cite this as:

Weisstein, Eric W. "Rational Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RationalTriangle.html