Some Unique Pythagorean Triples


Some Ways To Work With Them

Some natural numbers or counting numbers such as 3, 4 and 5 will make the statement     a^2 + b^2 = c^2     TRUE   when substituted for a, b and c! Then a = 3/5 and b = 4/5 will make c = __?__.

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?

Rational Points

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