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Foundations of Plane Geometry by Harvey I. Blau (2002, Hardcover)

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About this product

Product Identifiers

PublisherPrentice Hall PTR

ISBN-100130479543

ISBN-139780130479549

eBay Product ID (ePID)2287828

Product Key Features

Number of Pages298 Pages

LanguageEnglish

Publication NameFoundations of Plane Geometry

SubjectGeometry / General

Publication Year2002

TypeTextbook

AuthorHarvey I. Blau

Subject AreaMathematics

FormatHardcover

Dimensions

Item Height0.8 in

Item Weight18.3 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2002-030778

Dewey Edition21

IllustratedYes

Dewey Decimal516.22

Table Of Content 0. The Question of Parallels. 1. Five Examples. 2. Some Logic. 3. Practice Proofs. 4. Set Terminology and Sets of Real Numbers. 5. An Axiom System for Plane Geometry: First Steps. 6. Betweenness, Segments and Rays. 7. Three Axioms for the Line. 8. The Real Ray Axiom and Its Consequences. 9. Antipodes and Opposite Rays. 10. Separation. 11. Pencils and Angles. 12. The Crossbar Theorem. 13. Side-Angle-Side. 14. Perpendiculars. 15. The Exterior Angle Inequality and Triangle Inequality. 16. Further Results on Triangles. 17. Parallels and the Diameter of the Plane. 18. Angle Sums of Triangles. 19. Parallels and Angle Sums. 20. Concurrence. 21. Circles. 22. Similarity. Appendix I. Definitions and Assumptions from Book I of Euclid's Elements. Appendix II. The Side-Angle-Side Axiom in the Hyperbolic Plane. Bibliography. Index.

SynopsisFor junior/senior-level courses in Geometry. Ideal for students who may have little previous experience with abstraction and proof, this text provides a rigorous and unified yet straightforward and accessible exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes with a leisurely development that allows ample time for students' mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular.

LC Classification NumberQA455.B66 2002