Updates to Chapter 4, "Making Squares Dance",
in Hinged Dissections: Swinging & Twisting, by Greg N. Frederickson

Early hingeable demonstrations of Pythagorean Theorem

There were several early hingeable demonstrations of the Pythagorean Theorem, in:
James Clifton Eaves, "Pythagoras, his theorem and some gadgets", Mathematics Magazine, vol. 27, no. 3 (Jan-Feb 1954), pages 161-167.
Eaves gave three different gadgets. The second and third examples hinge the pieces of not only both squares but also the right triangle that is the basis of the particular example. Thus the demonstrations are not properly dissections in the sense that I use. Nonetheless, they are uniquely interesting.
Also, Eaves used what I would consider to be nonstandard hinges. First is what I called a lift hinge on page 222. Second is a hinge that allows overlap with a second hinge. I did not define this in my book, but Anton Hanegraaf had used such a hinge in one of his hinged dissections.

Attribution should go to Harry Bradley

In his solution to Problem 515 (Geometry), American Mathematical Monthly, volume 25 (1918), pages 23-24, Harry Bradley gave essentially the same dissection of three squares to one as the one that I gave on the right of Figure 4.11. There is no indication that Professor Bradley knew that the dissection is swing-hingeable.

Copyright 2003-2007, Greg N. Frederickson.
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Last updated July 13, 2007.