By Pythagoras' theorem, if a is the hypotenuse of a right triangle and b and c are the sides forming the right angle, then a2 = b2 + c2. These three numbers form a Pythagorean triple if they are integers for some choice of unit. The triangle is then rational, in the sense that the ratios of its sides are rational numbers. Conversely, a Pythagorean triple corresponds to a rational right triangle.
Fermat: a visionary remark
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The best-known Pythagorean triple, (3, 4, 5), corresponds to the thirteen-knot rope used by medieval builders to lay out right angles.
The thirteen-knot rope.
