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Geometry: Euclid and Beyond
BY [Robin Hartshorne]
Summary
Robin Hartshorne’s Geometry: Euclid and Beyond is a modern undergraduate treatment of classical geometry that begins with a critical study of Euclid’s Elements and develops its ideas using modern mathematical foundations. The book introduces Hilbert’s axioms, connects synthetic geometry with the Cartesian plane and algebraic fields, and explores segment arithmetic, area, geometric construction problems, and the role of field extensions in determining which ruler-and-compass constructions are possible.
A major part is devoted to the parallel postulate and non-Euclidean geometries, showing how changing fundamental assumptions produces different geometrical worlds, while the final chapter completes Euclid’s discussion of the five Platonic solids. Overall, Hartshorne presents geometry as a progression from Euclid’s classical methods to rigorous modern mathematics, while keeping the subject accessible to students with high-school geometry and some abstract algebra.
BOOK
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