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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 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.

In Japan pentagonal knots have also been used from an early date, possibly an earlier date, to fasten articles of clothing.

There is a separate page about Japanese Knotted Letters, the knots in which are sometimes pentagonal and sometimes not.

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In Japan

1723

This print, also by Nishikawa Sukenobu, from 'Joro Shina sadame', published n 1723, shows a pentagonal knot used to fasten the ties of a garment. The women in this print are members of the royal family.

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c1700 - 1750

This lacquered wooden box with a lid in the form of a pentagonal knot is held in the collection of the Victoria and Albert Museum in London.

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1758

This print from volume 1 of 'Ehon mitsuwa gusa', which was published in 1758, shows a document folded into a pentagonal knot laid in a box, possibly serving as a wrapper for some dried abalone.

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1768

In this print from 'Ehon ike no kawazu', which was published in 1768, the lady on the right is offering the man in front of her a stick to which a document is tied using a pentagonal knot.

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1899

In this print by Mizuno Toshikata from the picturebook 'Imayo bijin' which was published in 1899 the squatting woman's hair is secured using a pentagonal knot.

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In Western Europe / the USA

1668

The article shown below was printed on page 11 of issue 272 of the French journal 'Les Feuilles Marcophiles' in 1993. It shows two notes or letters which have first been folded into narrow strips and then into pentagonal knots and addressed on the outside, presumably for delivery by hand. The unfolded verso and recto of the left hand knot are also shown. Neither document bears a date. The article states that the assigned date of 1668 has been determined from other documents in the same archive. The name of the archive, however, is not given. My thanks to Michel Grand for this information.

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1682

A description of how to fold a pentagonal knot appears in the 1682 second 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 and did not appear in the 1656 first edition. (The second paragraph explains how to fold a hexagonal knot.)

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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1891

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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1892

The same design also occurs in 'Le Travail Manuel a L'ecole Primaire' by Jully & Rocheron, which was published by Librairie Classique Eugene Belin in Paris in 1892.

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1893

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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1904

The Pentagonal Knot appears in 'Guia Practica del Trabajo Manual Educativo' by Ezequiel Solana, which was published by Editorial Magisterio Español in Madrid in 1904, as a way of constructing a regular pentagon.

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1928

On 26th June 1928 Miguel de Unamuno wrote a poem which refers to the pentagonal knot / pentagram:

'Dios jugando con los dobles / cinco dedos de ambas manos / anudó cinta de yerba; / de cinco puntas fue el lazo. / De donde sacó la estrella / pentagonal, que sus brazos / dio a la blancas frescas alas / de la rosa del garbanzo.'

In English, roughly:

'God playing with the doubles / five fingers of both hands / knotted weed tape; / Five-pointed was the loop. / Where did he get the star / pentagonal, than his arms / He gave the fresh white wings / of the garbanzo rose.'

This poem was included in 'Cancionero' (Songbook), a collection of Don Miguel's poetry published posthumously in 1953.

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1931

The Pentagonal Knot appears as a puzzle in '536 Puzzles and Curious Problems by Henry Dudeney' which was a combination of almost all the material previously published in his 'Modern Puzzles' (published in 1926) and 'Puzzles and Curious Problems' (published in 1931), edited into a single volume by Martin Gardner, and published by Charles Scribner's Sons in New York in 1976. Unfortunately Gardner does not say in which of the volumes each of the puzzles originally appeared.

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1932

'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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1933

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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1940

'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940 as a way of constructing a regular pentagon.

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1959

Both the Pentagonal Knot and the See-Through Pentagram were explained in an article titled 'About origami, the Japanese art of folding objects out of paper' by Martin Gardner which appeared in the July 1959 issue of 'Scientific American'.

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