Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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The Pentagonal Knot and the See-Through Pentagram
 
This page attempts to record what is known about the origin and history of the origami design known as the Pentagonal Knot and its derivation, the See-Through Pentagram. Please contact me if you know any of this information is incorrect or if you have any other information that should be added. Thank you.

This design appears to have been known at an early date in both Western Europe and Japan. Early information has not yet been added to this page.

In Japan

In Western Europe

A description of this design first appears in the 1682 edition of 'Trattato Della Sfera' in a section called 'Prattische Astronomonische. Intorno all circoli della Sfera' which was an addition to the original work by Urban d'Aviso.

This 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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The Pentagonal Knot was published in L'Illustration 2527 of 1st August 1891 and subsequently included in the second volume of 'La Science Amusante' by Tom Tit (real name Arthur Good), which was published in Paris by Librairie Larousse in 1892.

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The Ring of Five Pentagonal Knots was published in L'Illustration 2613 of 26th March 1893 and subsequently included in the third volume of 'La Science Amusante' by Tom Tit (real name Arthur Good), which was published in Paris by Librairie Larousse in 1893.

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'Winter Nights Entertainments' by R M Abraham, which was first published by Constable and Constable in London in 1932, contains diagrams for the Pentagonal Knot under the title 'Here Is Another Method'. This title refers to the previous design in the book which was introduced with the words 'Here is one of the ways our grandmothers folded their love-letters ...'

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R M Abraham's follow up book, 'Diversions and Pastimes', which was first published by Constable and Constable in London in 1933 included the See-Through Pentagram under the title of 'Five-Pointed Star'.

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