Exceptionally well–written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof–oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An excellent introduction to advanced concepts as well as a reference to techniques for use in independent study and research, Methods of Geometry also features:
- Ample exercises designed to promote effective problem–solving strategies
- Insight into novel uses of Euclidean geometry
- More than 300 figures accompanying definitions and proofs
- A comprehensive and annotated bibliography
- Appendices reviewing vector and matrix algebra, least upper bound principle, and equivalence relations
Elementary Euclidean Geometry.
Exercises on Elementary Geometry.
Some Triangle and Circle Geometry.
Plane Isometries and Similarities.
Three Dimensional Isometries and Similarities.
"Fine interweaving of history, foundations, and geometry.... Useful as a source of exercises." (American Mathematical Monthly, November 2001)