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Beyond Pythagoras The numbers 3,4 and 5 satisfy the condition; 3+4=5 Because 3=3x3=9 4=4x4=16 5=5x5=25 Therefor The numbers 5,12 and 13 also satisfy the condition; 5+12=13 Because 5=5x5=25 12=12x12=144 13=13x13=169 Therefor And the numbers 7,24 and 25 satisfy the condition too; 7+24=25 Because 7=7x7=49 24=24x24=576 25=25x25=625 Therefor The units 5,12 and 13 can be lengths-in appropriate units-of a right-angled triangle The Perimeter = 5+12+13= 30 units The Area x5x12= 30 units The units 7,24 and 25 can also be length in appropriate units-of a right-angled triangle The Perimeter = 7+24+25= 46 units And the Area = x7x24= 84 Length of shortest side Length of middle side Length of longest side perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 46 84 9 40 41 90 180 11 58 61 130 319 There are relatively easy patterns to work out; the length of the shortest side, the length of the middle side and the length of the longest side but not to the perimeter or the area. The shortest length pattern is 2n+1, the pattern equation for the middle length is 2n2+2n and the pattern equation for the longest side is 2n2+2n+1. At first I thought it would not be possible to create...

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