Ebay Eureka!
On ebay, a vendor recently was trying to sell the cover to an 1876 game called Pythagoras Blocks or Finger Geometry
The game involved educational blocks that could be arranged into a 4" x 4" square.
By doing some research (Wisconsin Journal of Education, 1876, and the Michigan Teacher, Jan. 1876), I learned that the Pythagorean Blocks were created by Mr. R. R. Calkins from St. Joseph, MO, who claimed that this "new and ingenious device of five blocks...demonstrate to the eye, if rightly put together, the 47th problem of Euclid." You may recognize this problem by its other name, the Pythagorean Theorem.
On further research (Indiana School Journal, 1876), I learned that the Pythagorean Blocks consist of three rightangled triangles, one trapezoid, and one trapezium. Not only do they form a single square...but they form it in two ways.
Can you figure out how to dissect a square into these five pieces such that they not only can be arranged in a different way to form another square...but also illustrate a proof of the Pythagorean Theorem?
Solution:
