Updates to Chapter 7, "Who's the Squarest of Them All?",
in Hinged Dissections: Swinging & Twisting, by Greg N. Frederickson

Early hingeable demonstrations of 3-4-5 Squares

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 hinged the pieces of not only both squares but also the right triangle that was the basis of the particular example. Thus the demonstrations are not properly dissections in the sense that I have used. Eaves uses seven pieces, including the right triangle, in illustrating the 3-4-5 identity. However it is possible to modify my Figure 7.1 by adding the right triangle. (Puzzle: See how to hinge it to the two assemblages.) Thus one needs at most five pieces.

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