The Elements of Non-Euclidean Plane Geometry and Trigonometry (Classic Reprint) - Softcover

Inhaltsangabe

Explore how geometry broke free from the parallel postulate and opened new worlds of shape and space. This non‑Euclidean journey surveys the ideas, proofs, and key contributors that revealed consistent alternatives to Euclid’s classical geometry, from early debates to modern formulations.

Beginning with the historic question of parallels, the book traces how mathematicians like Bolyai, Lobachevsky, Gauss, and Riemann expanded geometry beyond Euclid. It introduces hyperbolic and elliptic planes, theorems on parallels, trigonometry, and the tools used to measure length and area in these new settings. The work balances historical context with clear explanations of constructions and the logic behind non‑Euclidean systems.

• Foundational ideas about the parallel postulate and its alternatives


• Step-by-step constructions in hyperbolic and elliptic geometries


• Theory and formulas for hyperbolic plane trigonometry and area


• Historical development and the search for consistency and truth in geometry

Ideal for readers interested in the history and foundations of geometry, and for those who want a solid introduction to non‑Euclidean ideas alongside their historical context.

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