Congruent Numbers

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A positive integer is called congruent if it is the area of a right triangle whose side lengths are rational numbers.

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For example, the right triangle with legs 20/7 and 357/5 has area 102, and the hypotenuse 2501/35 is rational, so 102 is a congruent number. This Demonstration shows representative triangles for all known congruent numbers under 1000. Finding a triangle for area is equivalent to solving the elliptic curve . Completely solving this problem is similar to solving the Birch and Swinnerton-Dyer conjecture, which is an unsolved problem with a million-dollar prize.

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Contributed by: Ed Pegg Jr (November 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Data for these triangles is from [1].

References

[1] M. Fiorentini. "Numeri Congruenti Minori di 1000." bitman.name/math/table/29.

[2] Wikipedia. "Congruent Number." (Mar 14, 2013) en.wikipedia.org/wiki/Congruent_number.



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