Abstract

We assess selected geometric dissections associated with, or inspired by, Ernest Irving Freese’s 1957 manuscript and identify noteworthy features that lay beneath their surface. These include a dissection of a regular dodecagon to a regular hexagon, a hingeable dissection of a Greek Cross to an equilateral triangle, a hingeable dissection of an equilateral triangle to a regular hexagon, a hingeable dissection of ten regular pentagons to a decagonal ring, a translational dissection of two regular decagons to one, a translational dissection of a dodecagram and a co-dodecagram to a regular dodecagon, a translational dissection of ten regular pentagons to two 5-pointed pseudo-stars and a regular decagon, a translational dissection of ten regular heptagons to four 7-pointed pseudo-stars and a regular 14-gon, a translational dissection of three regular octagons to a larger octagon, a hingeable dissection of regular pentagons for (sin π/5)2 + (cos π/5)2 = 1, a translational dissection of squares of areas 1, 3, 5, 7, 9, and 11 to a large square, and a translational dissection of squares for 82 + 92 + 122 = 172. Unsubstantiated claims by Freese are also evaluated.

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