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This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.

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• Division Ratios and Triangles: Elementary Euclidean Geometry
• Division Ratios
• Menelaus Theorem
• Cevas Theorem
• The Euler Line
• The Nine-Point Circle and the Equicircles
• Circles and Directed Distances
• TransformationGeometry: Isometries
• Wallpaper Groups and Translations
• Axes and Centers of Wallpaper Groups
• Wallpaper Groups without Rotations
• Wallpaper Groups with 90 Rotations
• Wallpaper Groups with only 180 or with 120 Rotations
• Dilations
• Projective Geometry: The Extended Plane
• Pappus Theorem and Projections Between Planes
• Desargues Theorem and Duality
• Harmonic Sets
• Triangles and Conic Sections
• Conic Sections: Cross-Ratios
• Polygons Inscribed in Conic Sections
• Graphs of Quadratic Equations
• Characterizations of Conic Sections
• Axiomatic Geometry: Inversion in Circles
• The Hyperbolic Plane
• Absolute Geometry
• Axiomatic Euclidean and Hyperbolic Geometry
• Index

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CHOICE Review

In the undergraduate curriculum, geometry has a dual status. It is both the subject that will be taught by future teachers of high school mathematics, and a modern topic that builds on advanced analysis and linear algebra with its own problems and techniques. The type of course taught at any given institution is determined by its needs. Bix offers a substantial book for prospective high school teachers. The choice of topics--elementary Euclidean geometry, transformation geometry, projective geometry, conic sections, and non-Euclidean geometry--does not distinguish the book from its many competitors. However, the level of exposition and the author's careful presentation of material distinguish it from an approach other authors take that can only be called condescending. Bix exposes his story carefully, introducing the appropriate ideas to give a complete accounting of the main results. The book, a real mathematical text, is rich because the subject is rich and the author has not taken shortcuts. The historical remarks and copious exercises add to the fine exposition. A welcome addition to the undergraduate-level library, especially wherever future teachers of geometry are found. J. McCleary; Vassar College