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Sheila LaBoof started this discussion 10 years ago#54,038
This is interesting: the numbers 44, 117, and 240, when taken two at a time as legs of a right triangle, each have a whole number hypotenuse.
44 and 117 have 125
44 and 240 have 244
117 and 240 have 267
Also, there exists at least one pythagorean hexahedron: a sixed-faced polyhedron each of whose faces is a right triangle of whole number lengths. You can construct it by making a central base triangle with lengths 1105, 1073, and 264, and then extending edges up by 448, 520, and 975 to a point to create three triangles of the hexahedron, and also extending edges down 495, 561, and 952 to a point to create the other three triangles of the hexahedron.
bhutto joined in and replied with this 10 years ago, 6 minutes later[^][v]#703,562
ugh upgrade to 3 4 5 triangles #blackmathmatters
Sheila LaBoof (OP) replied with this 10 years ago, 9 minutes later, 16 minutes after the original post[^][v]#703,566
question: having seen the example of a set of 3 whole numbers, are there sets of 4, or 5, etc. whole numbers whose every pair taken as shorter legs of a right triangle produces a whole number hypotenuse?
bhutto replied with this 10 years ago, 4 minutes later, 20 minutes after the original post[^][v]#703,568