Isosceles Dudeney
- Edwin Corrie
- Sep 3
- 1 min read
Updated: Oct 26
This is a brief follow-on to my last post dealing with Henry Dudeney's Haberdasher's Puzzle, a classic geometric dissection of an equilateral triangle into four pieces that can be reassembled to form a square.
The two origami versions of the puzzle by David Petty and Jeremy Shafer were based on an isosceles triangle rather than an equilateral one. Thanks to Greg N. Frederickson's book on the amazing work of Ernest Irving Freese I learned that in fact this is a more general form of the well known triangle-to-square dissection.
From Ernest Irving Freese's Geometric Transformations (2018) by Greg N. Frederickson
Of the two variants reproduced here from the Freese manuscript, the top one corresponds pretty closely to the Petty and Shafer designs. The bottom one with its easy reference points also looked like a good candidate for an origami rendering, and although it turned out to be a bit more challenging than it originally seemed I managed to work something out, so for the sake of completeness I'm posting my solution here.
For more on a wide range of pure non-origami geometric dissections, see Recreational Problems in Geometric Dissections & How to Solve Them (1972) by Harry Lindgren and Greg N. Frederickson, which is a revised edition of Harry Lindgren's pioneering 1964 book Geometric Dissections. There are also several more recent works by Greg N. Frederickson, details of which can be found on His website at https://www.cs.purdue.edu/homes/gnf/.