09-22-2026, 05:09 PM
Arthur Baragar’s A Survey of Classical and Modern Geometries: With Computer Activities (2001) is an intermediate-level geometry textbook that develops geometry from both historical and modern perspectives. It begins with Euclidean geometry, including axioms, classical theorems, Greek astronomy, compass-and-straightedge constructions, and the use of dynamic geometry software such as Geometer’s Sketchpad.
It then expands into higher-dimensional objects, Platonic and semiregular solids, and the mathematical foundations underlying geometric concepts. The book is designed not merely to present results but to cultivate geometric intuition through models, constructions, exercises, and computer experimentation.
The central part of the book explores the transition from Euclidean to non-Euclidean and modern geometries. Baragar develops hyperbolic geometry and its Poincaré models, including isometries, inversion, fractional linear transformations, hyperbolic trigonometry, and curvature; he then examines tilings and lattices, spherical and elliptic geometry, projective geometry, the pseudosphere in Lorentz space, finite geometries, and questions of constructibility.
The final material connects these classical subjects with modern research in geometry, emphasizing how changing fundamental assumptions—especially the parallel postulate—produces entirely different but internally consistent geometrical worlds.
BOOK
It then expands into higher-dimensional objects, Platonic and semiregular solids, and the mathematical foundations underlying geometric concepts. The book is designed not merely to present results but to cultivate geometric intuition through models, constructions, exercises, and computer experimentation.
The central part of the book explores the transition from Euclidean to non-Euclidean and modern geometries. Baragar develops hyperbolic geometry and its Poincaré models, including isometries, inversion, fractional linear transformations, hyperbolic trigonometry, and curvature; he then examines tilings and lattices, spherical and elliptic geometry, projective geometry, the pseudosphere in Lorentz space, finite geometries, and questions of constructibility.
The final material connects these classical subjects with modern research in geometry, emphasizing how changing fundamental assumptions—especially the parallel postulate—produces entirely different but internally consistent geometrical worlds.
BOOK
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