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My uncle Leon has an alternative version of plane geometry and it shows Euclid was all wrong.
His penchant for drawing inspiration from a complex interplay of lived experience, plane geometry and other art is confirmed by a large gallery devoted to more than two dozen paintings, reliefs and works on paper from the museum's collection (including several recent acquisitions).
Eventually it was realized that geometry need not be limited to the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry) but that even the most abstract thoughts and images might be represented and developed in geometric terms.
Those include a work on inscribing the regular heptagon in a circle; a collection of lemmas (propositions assumed to be true that are used to prove a theorem) and a book, On Touching Circles, both having to do with elementary plane geometry; and the Stomachion (parts of which also survive in Greek), dealing with a square divided into 14 pieces for a game or puzzle.
It may be that being familiar with solid geometry is a disadvantage when first approaching the problem, because then you are apt to expect that the faces of the objects are going to meet at some weird angles (not the nice 90 or 60 or 45 degree angles you get in plane geometry), and there is no obvious reason to think that the angles in the tetrahedron would be related to those in the pyramid.
In 1959, the famous origami exhibition, "Plane Geometry and Fancy Figures," was held in the United States, taking place at The Cooper Union in New York.
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CEO of Professional Science Editing for Scientists @ prosciediting.com