The Pythagorean Theorem - Educational Outreach

The last equality shows that the inscribed radius ris a product of two positive integral quantities n( m n).Thus the inscribed radius itself, called a PythagoreanRadius, is a positive integral quantity, which is what we setout to prove. The proof also gives us as a bonus the actualformula for finding the inscribed radius r n( m n).Table 3.5 gives r values for all possible m & n values wherem 7 .M N A=2MN B=M 2 -N 2 C=M 2 +N 2 R=N(M-N)2 1 4 3 5 13 1 6 8 10 23 2 12 5 13 24 1 8 15 17 34 2 16 12 20 44 3 24 7 25 35 1 10 24 26 45 2 20 21 29 65 3 30 16 34 65 4 40 9 41 46 1 12 35 37 56 2 24 32 40 86 3 36 27 45 96 4 48 20 52 86 5 60 11 61 57 1 14 48 50 67 2 28 45 53 107 3 42 40 58 127 4 56 33 65 127 5 70 24 74 107 6 84 13 85 6Table 3.5: Select Pythagorean Radii97