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Which regular polygons does Euclid construct in Book IV of the Elements?
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Euclid
Euclid, coloured woodcut, 1584. His Elements, a treatise on geometry and mathematics, is one of the most influential books ever written.
In Book IV of the Elements, Euclid focuses on the construction of various regular polygons inscribed within circles using only a compass and an unmarked straightedge.12
While the book covers the construction of several figures, it is particularly noted for its detailed treatment of the pentagon. The constructions presented in Book IV are associated with the work of the Pythagoreans and represent a significant portion of the foundational plane geometry established in the Elements.2