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Last updated 18/8/2024

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'Trattato Della Sfera' by Urban d'Aviso was originally published in 1656. The revised 1682 second edition contains an additional section called 'Prattische Astronomonische. Intorno all circoli della Sfera' which explains how to fold a pentagonal and a hexagonal knot from a strip of paper.

The first paragraph is translated in John Sharp's article 'Folding the Regular Pentagon' (BSHM Bulletin: Journal of the British Society for the History of Mathematics,31:3,179-188, 2016) as 'On the subject of drawing these figures, I want to give a way of describing, and forming mechanically, a Pentagon, which is one of the most difficult figures to draw, nevertheless it is the easiest, since it is found in nature ... because it is none other than a simple knot. You would take, for instance, a strip of paper, of whatever thickness you want, and which has two parallel sides, and with this proceed to make a knot, as if the paper were a cord, being attentive, however, that, first the paper is always in the same folds, and, second, that it is tightened sufficiently to remain well stretched. If you were now to cut the ends which stick out, with some scissors, you would have a most true pentagon.'

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