Geometric Models – Plane Dissections

To illustrate the Pythagorean Theorem, makers of geometric models have long made models with pieces that could be arranged either as a square with a side equal to the length of the hypotenuse of a right triangle or as two squares, with sides equal to the length of the two other sides of the triangle. In 1928, R. H. Wood, a student of high school teacher A. Harry Wheeler in Worcester, Massachusetts, made such a model.

Any two polygons of equal area can be divided into a finite number of polygonal pieces that can be arranged to form either polygon. This result was well known from the mid-1800s. A few model makers, such as Wheeler, took great delight in developing specific models of dissected polygons and figuring out different ways to arrange the pieces. Surviving notes from the early 1930s indicate that Wheeler designed models of relatively complicated plane dissections for his own pleasure. Then, mindful of the popularity of jigsaw puzzles in the Depression years, he made and encouraged his students to make dissections of simpler forms. Some of these models were hinged at vertices.

Wheeler classified his dissections according to the number of pieces used. The arrangement of records below follows this scheme. In some instances, pieces that fit together were assigned separate numbers. The separate records have been kept, with text indicating what fits together. Records on documentation relating to these models are at the end of the group. Throughout, clicking on the title of an object brings up further images and description.


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