Fold-and-cut theorem

The earliest known description of a fold-and-cut problem appears in Wakoku Chiyekurabe (Mathematical Contests), a book that was published in 1721 by Kan Chu Sen in Japan.

[2] An 1873 article in Harper's New Monthly Magazine describes how Betsy Ross may have proposed that stars on the American flag have five points, because such a shape can easily be obtained by the fold-and-cut method.

[3] In the 20th century, several magicians published books containing examples of fold-and-cut problems, including Will Blyth,[4] Harry Houdini,[5] and Gerald Loe (1955).

Examples mentioned by Gardner include separating the red squares from the black squares of a checkerboard with one cut, and "an old paper-cutting stunt, of unknown origin" in which one cut splits a piece of paper into both a Latin cross and a set of smaller pieces that can be rearranged to spell the word "hell".

[8][9] There are two general methods known for solving instances of the fold-and-cut problem, based on straight skeletons and on circle packing respectively.

Creating a Koch snowflake curve by the fold-and-cut method
Creating a Koch snowflake curve by the fold-and-cut method
Creating an anti-Koch snowflake curve by the fold-and-cut method
Creating an anti-Koch snowflake curve by the fold-and-cut method