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Puzzles in trigonometry Aspects of triangles and circles continue to interest members. Dudley Dennington acknowledges that he is another in a long line of contributors, and writes from Surbiton in Surrey: In Verulam (l8 November 1997) your correspondents do not mention the set of right-angled triangles, which appears to be infinite, in which integral shorter sides differ by one. I have established this up to N = 15. The set is interesting in that, unlike the familiar ones which have been quoted, the triangles get marginally ‘steeper’ as the sides get longer rather than ‘flatter’, approaching an equilateral shape. As usual, 3:4:5 turns up.