Pythagorean triples {a, b, c} will give rational points (a/c, b/c) on a unit circle. The slope of a line from the point (0, 0) to this point (a/c, b/c) is an interesting review of "slope" concepts in algebra and calculus and "angles" in the study of trigonometry.

But a very large set of right triangle puzzle pieces with one side congruent may make an interesting jigsaw puzzle for your family holiday. Example: {3, 4, 5} with {5, 12, 13} each have a side of 5. Find a unique pythagorean triple with a side of 12 and you are on your way. Do those triangles in the {3, 4, 5} chain ever share a side in common with ones in the {8, 15, 17}, {17, 144, 145}, {7, 24, 25}, and {24, 143,145} net?