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It is possible to draw a whole series of lengths that are irrational by following the pattern in the diagram below and using Pythagoras’ Theorem. Continue the diagram to produce lengths of 3, 5, 6, 7, etc. See how many you can draw. You should get an interesting shape. 1 2 1 1
1 1 1 1 1 10 1 11 9 1 12 8 13 7 1 1 14 6 15 1 1 5 16 1 4 2 1 1 3 17 1 1 18 1 1