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Recent Flourishing in Geometric Dissections

 

In 1964 an Australian, Harry Lindgren, published Recreational Problems in Geometric Dissections: And How to Solve Them. In 1972 the book was republished by a  geometric dissections enthusiast, Greg Frederickson, who went on to break remarkable new ground in the field, in three books published over the last decade.

In his booklet, Lindgren systematized practical methods for obtaining various dissections.[1] He called the most basic construction a P-strip, for “parallelogram-strip,” to designate a recurring pattern that serves to dissect a figure by superimposition. The word parallelogram should be understood in a generic sense, not literally; in fact, the patterns on the strips do not necessarily begin or end in straight lines.

Here are several examples of P-strips, from the simplest to more complex:[2]




Using P-strips, dissections can be formed by overlapping, as in the following examples of PP-dissections:

 

 

ENDNOTES:

 

[1] His ingenious methods are now available online on a web site set up by Gavin Theobald; it is also the source for our figures in this subsection.

[2] Source: http://home.btconnect.com/GavinTheobald/HTML/P-Strips.html

 

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