Beyond Pythagoras

... Beyond Pythagoras Sides (smallest number) 2 + (middle number) 2 =(largest number) 2 To test this: Perimeter Smallest number + middle number + largest number = perimeter To test this: Area 1/2 x smallest number x middle number = area To test this: Length of the shortest side Length of the middle side Length of the longest side Perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 56 84 9 40 41 90 180 11 60 61 132 330 13 84 85 182 546 15 112 113 240 840 17 144 145 306 1224 I managed to fill in the rest of the sides without using a formula by firstly for the shortest side add on two units to the value before. For the middle side the difference between each value is positive four units. For the longest side I added I=one unit to the value of the middle side in the same sequence. I have also noticed that the middle values are the triangle numbers multiplied by four. Also the second difference between each of the perimeter values is eight units. In the area the third difference between each of the values is twelve units. Shortest side I have worked out the

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