Abstract
to the 'vector' (3,4,5). A(3,4,5) = (5,12,13), A(5,12,13) = (7,24,25), .. ., A(an 1, bn-1, cn-1) = (an, bn, cn). It is a simple matter to check the validity of (1). Figures similar to the one shown may be drawn by using other sequences of triangles satisfying (1). For example, had we started with (a1, b1, c1) = (8, 15, 17) the successive application of A would generate the sequence (8,15,17), (12,35,37), (16,63,67),... . The innernost square is now 7 X 7. We note that cn bn= 2, whereas in the first example cn -bn = 1; cn bn is, in fact, invariant under A.
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