The Public Paperfolding History Project

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Fold and One Cut Designs
 
This page attempts to set out what is known about the history of Fold and One Cut Designs,in which the paper is folded in such a way that it is possible to obtain a given shape with just a single straight cut. Such designs are frequently presented as puzzles. Please contact me if you know that the information on this page is incorrect or if you know of important omissions. Thank you.

There is a separate page for Fold and One Cut Polygons (both regular convex shapes and stars).

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1721

The earliest known example of a Fold and One Cut Design (in fact a Fold and One Cut Design presented as a puzzle) occurs in the book 'Wakoku Chiyekurabe' (Mathematical Contests) by Kan Chu Sen which was published in Japan in 1721.

The target shape bears a distinct resemblance to the kamon (family badge) of the Ogasawara family shown below (see https://www.samurai-archives.com/crest5.html).

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Fold and One Cut Latin Crosses / Altar / Ticket to Heaven - 1833 onwards

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Fold and One Cut Hexagons - 1863 onwards

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The Fold and One Cut Pentagram - 1873 onwards

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Fold and One Cut Maltese Crosses - 1881 onwards

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Fold and One Cut Octagons

1887

As far as I know a method of making a fold and one cut octagon first appears in part 2 'Die Praxis' of 'Theoretisches und praktisches Handbuch der Fröbelschen Erziehungslehre' by Bertha von Marentholtz-Bülow, which was published by George H Wigand in Kassel in 1887.

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1892

This design appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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1892

The Fold and One Cut Equilateral Triangle and Three Pointed Star - 1892

These designs appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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The Fold and One Cut Four Pointed Star - 1892

This design appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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The Fold and One Cut Pentagon - 1892

These designs appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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Fold and One Cut Hexagrams (Stars of David) - 1892 onwards

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The Fold and One Cut Heptagon and Heptagram - 1892

These designs appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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The Fold and One Cut Octagram - 1892

This design appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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The Fold and One Cut Nonagon and Nonagram - 1892

These designs appeared in 'Paper Folding and Cutting' by Katherine M Ball, which was published by the Prang Educational Company in Boston in 1892.

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The Fold and One Cut Ladder - 1892 onwards

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