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Johannes Kepler discovers two of the Kepler-Poinsot polyhedra
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Carl Friedrich Gauss proves that the regular 17-gon can be constructed using only a compass and straightedge
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Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,
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– Pierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and straightedge, as well as the full completion of the problem of constructibility of regular polygons
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that for geometry you wont need polygons to help you
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