By Thomas Q. Sibley
Pondering Geometrically: A Survey of Geometries is a well-written and complete survey of faculty geometry that will serve a wide selection of classes for either arithmetic majors and arithmetic schooling majors. nice care and a focus is spent on constructing visible insights and geometric instinct whereas stressing the logical constitution, historic improvement, and deep interconnectedness of the ideas.
Students with much less mathematical guidance than upper-division arithmetic majors can effectively research the subjects wanted for the instruction of highschool academics. there's a multitude of routines and initiatives in these chapters constructing all elements of geometric considering for those scholars in addition to for extra complex scholars. those chapters contain Euclidean Geometry, Axiomatic platforms and types, Analytic Geometry, Transformational Geometry, and Symmetry. themes within the different chapters, together with Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, supply a broader view of geometry. the various chapters are as self reliant as attainable, whereas the textual content nonetheless manages to focus on the various connections among topics.
The textual content is self-contained, together with appendices with the fabric in Euclid’s first ebook and a highschool axiomatic procedure in addition to Hilbert’s axioms. Appendices provide short summaries of the elements of linear algebra and multivariable calculus wanted for definite chapters. whereas a few chapters use the language of teams, no earlier adventure with summary algebra is presumed. The textual content will help an technique emphasizing dynamical geometry software program with out being tied to any specific software program.