The Geometric Viewpoint
A Survey of Geometries
Published on 9. November 1998
Book
Hardback
309 pages
978-0-201-87450-1 (ISBN)
Description
This survey text with a historical emphasis supports several different courses. It includes group projects involving the use of technology or verbal/written responses. The text strives to build both students' intuition and reasoning. It is ideal for junior and senior level courses.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Weight
1000 gr
ISBN-13
978-0-201-87450-1 (9780201874501)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
1. Euclidean Geometry.
Overview and History.
Constructions, Congruence, and Parallels: Euclid's Approach to Geometry.
Biography: Archimedes.
A Critique of Euclid-Modern Axiomatics.
Biography: David Hilbert.
Axiomatic Systems, Models, and Metamathematics.
Similar Figures.
Three-Dimensional Geometry.
Projects for Chapter 1.
Suggested Readings.
Suggested Media.
2. Analytic Geometry
Overview and History.
Biography: Rene Descartes.
Conics and Locus Problems.
Biography: Pierre Fermat.
Further Topics in Analytic Geometry.
Curves in Computer-Aided Design.
Higher Dimensional Analytic Geometry.
Biography: Gaspard Monge.
Projects for Chapter 2.
Suggested Readings.
Suggested Media.
3. Non-Euclidean Geometries.
Overview and History.
Biography: Nikolai Lobachevsky and Janos Bolyai.
Biography: Carl Friedrich Gauss.
Biography: Georg Fredrich Bernhard Riemann.
Properties of Lines and Omega Triangles.
Saccheri Quadrilaterals and Triangles.
Area and Hyperbolic Designs.
Spherical and Single Elliptic Geometries.
Projects for Chapter 3.
Suggested Readings.
Suggested Media.
4. Transformational Geometry.
Overview and History.
Isometries.
Biography: Flex Klein.
Algebraic Representation of Transformations.
Similarities and Affine Transformation.
Biography: Sophus Lie.
Transformations in Higher Dimensions: Computer-Aided Design.
Inversions and the Complex Plane.
Biography: Augustus Mobius.
Projects for Chapter 4.
Suggested Readings.
Suggested Media.
5. Symmetry.
Overview and History.
Finite Plane Symmetry Groups.
Symmetry in the Plane.
Symmetries in Higher Dimensions.
Symmetry in Science.
Biography: Marjorie Senechal.
Fractals.
Biography: Benoit Mandelbrot.
Projects for Chapter 5.
Suggested Readings.
Suggested Media.
6. Projective Geometry.
Overview and History.
Axiomatic Projective Geometry.
Biography: Jean Victor Poncelet.
Analytic Projective Geometry.
Projective Transformations.
Subgeometries.
Biography: Arthur Cayley.
Projective Space.
Projects for Chapter 6.
Suggested Readings.
Suggested Media.
7. Finite Geometries.
Overview and History.
Biography: Leonhard Euler.
Affine and Projective Planes.
Design Theory.
Biography: Sir Ronald A. Fisher.
Finite Analytic Geometry.
Projects for Chapter 7.
Suggested Readings.
Appendices.
Definitions, Postulates, Common Notions, and Propositions from Book I of Euclid's Elements.
Hilbert's Axioms for Euclidean Plane Geometry.
Selected Answers.
Index.
Overview and History.
Constructions, Congruence, and Parallels: Euclid's Approach to Geometry.
Biography: Archimedes.
A Critique of Euclid-Modern Axiomatics.
Biography: David Hilbert.
Axiomatic Systems, Models, and Metamathematics.
Similar Figures.
Three-Dimensional Geometry.
Projects for Chapter 1.
Suggested Readings.
Suggested Media.
2. Analytic Geometry
Overview and History.
Biography: Rene Descartes.
Conics and Locus Problems.
Biography: Pierre Fermat.
Further Topics in Analytic Geometry.
Curves in Computer-Aided Design.
Higher Dimensional Analytic Geometry.
Biography: Gaspard Monge.
Projects for Chapter 2.
Suggested Readings.
Suggested Media.
3. Non-Euclidean Geometries.
Overview and History.
Biography: Nikolai Lobachevsky and Janos Bolyai.
Biography: Carl Friedrich Gauss.
Biography: Georg Fredrich Bernhard Riemann.
Properties of Lines and Omega Triangles.
Saccheri Quadrilaterals and Triangles.
Area and Hyperbolic Designs.
Spherical and Single Elliptic Geometries.
Projects for Chapter 3.
Suggested Readings.
Suggested Media.
4. Transformational Geometry.
Overview and History.
Isometries.
Biography: Flex Klein.
Algebraic Representation of Transformations.
Similarities and Affine Transformation.
Biography: Sophus Lie.
Transformations in Higher Dimensions: Computer-Aided Design.
Inversions and the Complex Plane.
Biography: Augustus Mobius.
Projects for Chapter 4.
Suggested Readings.
Suggested Media.
5. Symmetry.
Overview and History.
Finite Plane Symmetry Groups.
Symmetry in the Plane.
Symmetries in Higher Dimensions.
Symmetry in Science.
Biography: Marjorie Senechal.
Fractals.
Biography: Benoit Mandelbrot.
Projects for Chapter 5.
Suggested Readings.
Suggested Media.
6. Projective Geometry.
Overview and History.
Axiomatic Projective Geometry.
Biography: Jean Victor Poncelet.
Analytic Projective Geometry.
Projective Transformations.
Subgeometries.
Biography: Arthur Cayley.
Projective Space.
Projects for Chapter 6.
Suggested Readings.
Suggested Media.
7. Finite Geometries.
Overview and History.
Biography: Leonhard Euler.
Affine and Projective Planes.
Design Theory.
Biography: Sir Ronald A. Fisher.
Finite Analytic Geometry.
Projects for Chapter 7.
Suggested Readings.
Appendices.
Definitions, Postulates, Common Notions, and Propositions from Book I of Euclid's Elements.
Hilbert's Axioms for Euclidean Plane Geometry.
Selected Answers.
Index.