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The six first triangular numbers: 1, 3, 6, 10, 15, The th triangle in the sequence will have dots in the bottom row, and rows of dots. Confessions of a heterodox economist — Portsmouth, Hampshire. The argument is powerful, it generalises neatly to any size of triangle , and it reveals why the answer is what it is. For me, this idea of drawing the dots, duplicating, rotating and making a rectangle is beautiful. Edition: Available editions United Kingdom. Vicky Neale , University of Oxford. But here is one rather beautiful argument. I cannot find a piece of mathematics beautiful unless I first understand it properly — and that means it can take a while for me to appreciate the aesthetic qualities.

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