The Public Paperfolding History Project

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Constructing Hexagons by Folding Paper
 
This page attempts to record what is known about the history of methods of constructing hexagons by folding paper. 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.

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1682

A description of how to fold a hexagonal 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 first paragraph explains how to fold a pentagonal knot.)

The second paragraph can be translated, roughly, as 'You can also make a figure in the shape of a hexagon if you take two strips of paper of equal length, and with the sides parallel, and make a knot with them, making the tips of the curvature of one strip, pass through the opening of the curvature of the other, so that by tightening them properly, always keeping their width and cutting the leftovers of the tips, you will have made a true Hexagon.'

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1863

An illustration which depicts the construction of a hexagon from a bronze rectangle appears in 'De Kleine Papierwerkers 1: Wat men van een stukje papier al maken kan: Het vouwen' (The Small Paperwork 1: What one can make from a piece of paper: Folding) by Elise Van Calcar, which was published by K H Schadd in Amsterdam in 1863.

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1872

The second 'expanded and improved' edition of 'Das Frobel'sche Faltblatt' (Frobel's Folding Sheet) ) by August Kohler, which was published by Hermann Bohlau in Weimar in 1872, contains a method of constructing a regular hexagon by folding each corner inwards in turn to lie on the bisectors. I cannot find any reference to this technique in the text of the book.

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1873

'Die Praxis Des Kindergartens' by Auguste Koehler, which was published by Herman Bohlau in Weimar in 1873 contains a method of producing a regular hexagon by truncating a diamond folded from a square.

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1877

A method of making a regular hexagon from an equilateral triangle appears in 'Kindergarten Practice' by Mary Gurney, a substantially abridged version, in two parts, of 'Die Praxis Des Kindergartens' by Auguste Koehler. The second part, 'Froebel's Plane Surfaces', contains sections dealing with paper folding, cutting and weaving. The date of the first edition is not known. The second edition was published in 1877 in London by A N Myers and Co.

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The Fold and One Cut Hexagon - 1863 onwards

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1873

' Die Praxis Des Kindergartens' by Auguste Koehler, which was published by Herman Bohlau in Weimar in 1873 contains a method of producing a regular hexagon by truncating a diamond folded from a square..

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From a Mobius Band - 1893 onwards

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1940

Two methods of constructing a regular hexagon are found in '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.

From an equilateral triangle

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From a Rectangle

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