Hidden in Plane Sight: The Extraordinary Vision of Ernest Irving Freese

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.