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The cube is such a familiar object that few people know its formal name: the regular hexahedron. Yet that familiarity is deceptive... To see why, let’s slice a cube into sections: this old familiar shape still has a few surprises in store!
Discrete geometry is a recent field of research concerned with "discrete objects," such as graphs and tilings. But it also offers a fresh perspective on problems that are difficult to solve in a continuous setting, including the existence of regular polygons with integer-coordinate vertices.
Tilings and geometric dissections gave rise to equidissection puzzles, which have kept our brains buzzing since the 18th century.
Besides their undeniable aesthetic appeal, mosaics and other archaeological remains from our past often hold wonderful mathematical surprises. These geometric examples from Gallo-Roman sites offer ample proof.
