Thinking Geometrically

This is a self-contained, comprehensive survey of college geometry that can serve a wide variety of courses for students of both mathematics and mathematics education. The text develops visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Chapter topics include Euclidean geometry, axiomatic systems and models, analytic geometry, transformational geometry, symmetry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry, and discrete geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. Appendices include material from Euclid's first book, as well as Hilbert's axioms, and provide brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters.

• Emphasises the best aspects of geometrical thinking: its beauty, visual insights, convincing proofs, broad connections, and more
• The book's focus on developing reason and intuition will appeal to both students of mathematics and mathematics education
• Historical material and biographies of famous geometers share some of the rich insights that history can provide