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Geometry [Fenn] - mklabgr - 08-17-2026 Geometry Author: Roger Fenn Series: Springer Undergraduate Mathematics Series Publisher: Springer-Verlag London Publication: 2000/2001 Roger Fenn's Geometry is an undergraduate introduction designed to demonstrate both the accessibility and the surprising breadth of geometry. Fenn interprets geometry in its original sense of "world measurement," which explains the book's strong emphasis on numbers, coordinates, and algebraic methods alongside traditional geometric reasoning. Rather than restricting itself to elementary Euclidean geometry, the book gradually expands the reader's perspective from the geometry of numbers and coordinate methods to complex numbers, three-dimensional geometry, projective geometry, conics, spherical geometry, and even quaternions and octonions. The presentation aims to remain rigorous without assuming that every reader is already comfortable with advanced mathematics; more difficult material is deliberately distinguished so that it can be revisited on a later reading.  The progression of topics is particularly interesting. Fenn begins with the geometry of numbers, followed by coordinate geometry and classical Euclidean plane geometry. Complex numbers are then given a geometric interpretation before the discussion moves into solid and projective geometry. Later chapters cover conics and quadric surfaces, spherical geometry, and finally quaternions and octonions. Spherical geometry also provides connections with astronomy, including longitude and latitude, celestial coordinates, and related applications. This makes the book broader than a conventional undergraduate Euclidean-geometry text: it shows how algebra, number systems, coordinates, and transformations can all serve as languages for understanding geometric structures.  A major strength for students is the inclusion of more than 300 exercises, with answers supplied for most of them. Springer describes the book as appropriate not only for undergraduate geometry courses but also for advanced secondary students, physicists, introductory astronomy students, and even mathematicians looking for a general geometry reference.  Key takeaways Broad view of geometry: Fenn moves from numbers and coordinates through Euclidean, complex, solid, projective and spherical geometry. Geometry and algebra are closely connected: complex numbers, coordinates, quaternions and octonions demonstrate how algebraic structures acquire geometric meaning. Unusually wide undergraduate coverage: the final chapter on quaternions and octonions takes the reader well beyond what is normally encountered in an introductory geometry course. Strong self-study potential: more than 300 exercises, answers to most of them, and a presentation designed to allow difficult sections to be revisited make it a useful independent-study text.  Overall: ★★★★½ — A rich and somewhat unconventional undergraduate geometry book. It is especially attractive for readers who want to see geometry as a subject connecting classical constructions, coordinate methods, algebra, complex numbers, higher-dimensional objects, and astronomy, rather than as Euclidean geometry alone. Official Springer page for Roger Fenn's Geometry Goodreads page you originally provided