Geometry. - Second Edition

For centuries, geometry has provided the core examples to introduce students to the world of higher mathematics, its ways of thinking, its beauties, its concepts of theorem and proof, and its standards of rigor. This role has been transferred to other areas of mathematics over the last few decades, leaving geometry a relatively secondary and often intellectually barren subject in the mathematical curriculum. This text, inspired by the work and educational interests of a prominent research mathematician, and Gene Murrow's experience as a high school teacher, presents geometry in an exemplary and, to the student, accessible and attractive form. The book emphasizes both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. Neither is treated at the expense of the other. The book also teaches the student fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course. There are many examples and exercises.