Pythagorean triples as a grid

We are watching a Netflix series as Simon comes up to me and says: Mom, give me an odd number! I go, “All right, ahh, 13!” – He starts scribbling something in his sketch book. His Dad and I exchange meaningful glances, we know him too well not to pauze Netflix and wait patiently. Sometimes we try to say quietly, is this going to take long ’cause we are sort of in the middle of a movie here, but we know math goes first. “Look, I have Pythagorean Triples now!” Simon triumphs. “I simply square your number, then divide the result by two and the two numbers around that are the two missing numbers!.. Do you know how I see it? I basically imagine a grid, a 13 by 13 grid. ” (He starts drawing the grid). “Look and then it has 169 cells in it, and you try to divide it in two nearly identical grids, 84 and 85 cells in each… Hey Mom, do you know I can also make scaled Pythagorean Triples? ”

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