math puzzle
i like math puzzles. this one was inspired reading the barn to bennett. the smart kid was laying out the barn they were going to build before their dad died. he wanted nice square corners. so he knotted a rope into a 3-4-5 triangle. this led to some discussion as to why that made a right triangle. we got out the legos to verify it and to look for other special triangles. anywho, we did the sum of the squares thing. he was all like, huh. at one point he drew on the blackboard a right triangle with sides 4-5-6. which is wrong. at least on a plane. maybe on a sphere where the "straight lines" are arcs of great circles. the math puzzle is to figure out the radius of a sphere on which you can draw a 4-5-6 right triangle. it boils down to solving a rather pretty transcendental equation. which reduces to the pythagorean theorem when the radius of the sphere goes to infinity. maybe i'll post the equation in some later post. i'll give you a chance to derive it first. enjoy.