Geometry for College Students » (New Edition)

I. Martin Isaacs', author of the well-known ALGEBRA: A GRADUATE COURSE, has written a new text that will make readers appreciate the beauty of geometry, especially what it can teach about deductive reasoning and the nature of mathematical proofs. The author focuses on the two classic themes of geometry: facts and proofs.

Booknews

Written as a textbook for his college geometry course at the U. of Wisconsin-Madison, this volume is for college students who enjoyed but may not have retained much of their high-school geometry. Emphasizing "really pretty" theorems and their proofs rather than the typical text's formalism and axiomatic method, chapters cover the basics, triangles, circles and lines, Ceva's theorem, vector methods of proof, and geometric constructions; and include exercises. The suggested further reading list starts aptly enough with Euclid. Annotation c. Book News, Inc., Portland, OR (booknews.com)

1. THE BASICS Introduction and Apology / Congruent Triangles / Angles and Parallel Lines / Parallelograms / Area / Circles and Arcs / Polygons in Circles / Similarity 2. TRIANGLES The Circumcircle / The Centroid / The Euler Line, Orthocenter and Nine-Point Circle / Computations / The Incircle / Exscribed Circles / Morley''s Theorem / Optimization in Triangles 3. CIRCLES AND LINES Simson Lines / The Butterfly Theorem / Cross Ratios / The Radical Axis 4. CEVA''S THEOREM AND ITS RELATIVE Ceva''s Theorem / Interior and Exterior Cevians / Ceva''s Theorem and Angles / Menelaus'' Theorem 5. VECTOR METHODS OF PROOF Vectors / Vectors and Geometry / Dot Products / Checkerboards / A Bit of Trigonometry / Linear Operators 6. GEOMETRIC CONSTRUCTIONS Rules of the Game / Reconstructing Triangles / Tangents / Three Hard Problems / Constructible Numbers / Changing the Rules SOME FURTHER READING / INDEX