Geometry from Euclid to Knots (eBook)

Saul Stahl (Autor)

eBook Download: EPUB

2012
480 Seiten
Dover Publications (Verlag)
978-0-486-13498-7 (ISBN)

Infos

This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.

---

Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's statements with appropriate historical commentary and many exercises — more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems. In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.

Inhalt

Preface to the Dover EditionPreface1. Other Geometries: A Computational Introduction2. The Neutral Geometry of the Triangle3. Nonneutral Euclidean Geometry4. Circles and Regular Polygons5. Toward Projective Geometry6. Planar Symmetries7. Inversions8. Symmetry in Space9. Informal Topology10. Graphs11. Surfaces12. Knots and LinksAppendix A: A Brief Introduction to the Geometer's SketchpadAppendix B: Summary of PropositionsAppendix C: George D. Birkhoff's Axiomatization of Euclidean GeometryAppendix D: The University of Chicago School Mathematics Project's Geometrical AxiomsAppendix E: David Hilbert's Axiomization of Euclidean GeometryAppendix F: PermutationsAppendixG: Modular ArithmeticSolutions and Hints to Selected ProblemsBibliographyIndex

Produkt-Details

• Erscheint lt. Verlag: 23.5.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 160 x 160 mm
• Gewicht: 603 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: axiomatic geometry • Axioms • Circles • Classroom • Curriculum • Education • Elements • Euclidean Geometry • geometric shapes • Geometry • Graphs • high school math • Hyperbolic Geometry • Informal topology • Inversions • knots • knot theory • Links • math teachers • non euclidean geometry • Plane Geometry • polygons • practice exercises • practice problems • Problem Solving • Projective Geometry • Reference • spherical geometry • Surfaces • Symmetries • Textbook • transformation geometry
• ISBN-10: 0-486-13498-9 / 0486134989
• ISBN-13: 978-0-486-13498-7 / 9780486134987