If the book could only have been longer (and my endurance greater!) I could have included much additional material. Here is an indication as to what was left out or was discovered too late.
Martin Gardner has made a nifty dissection from a curious fact: Take a square and draw the largest equilateral triangle that fits inside the square. (The triangle will share one vertex with the square, and have the two incident sides be 15 degrees from the square's incident sides.) Removing the equilateral triangle from the square leaves three right triangles. One is an isosceles right triangle, and it is equal in area to the sum of the areas of the other two.
Martin has found a 4-piece dissection of these two smaller right triangles to the isosceles right triangle. (His dissection turns a piece over, but I have modified it so that no pieces are turned over.) See "Gardner's Gatherings" in the September and October issues of Math Horizons. Looked at differently, his dissection gives a 6-piece dissection of a square into an equilateral triangle and a smaller square.
Copyright 1997, Greg N. Frederickson.
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Dissections: Plane & Fancy
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Last updated January 28, 1998.