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Geometry

Our Cultural Heritage

  • Textbook
  • © 2010

Overview

Authors:
  1. Audun Holme

    1. University of Bergen, Department of Mathematics, Bergen, Norway

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  • A very readable short history of geometry
  • No prerequisites required
  • Easy to understand by beginners
  • New edition with large number of exercises with some suggestions for solutions
  • Includes supplementary material: sn.pub/extras

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xvii
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  2. A Cultural Heritage

    1. Front Matter

      Pages 1-1
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    2. Early Beginnings

      • Audun Holme
      Pages 3-6

    3. The Great River Civilizations

      • Audun Holme
      Pages 7-29

    4. Greek and Hellenic Geometry

      • Audun Holme
      Pages 31-73

    5. Geometry in the Hellenistic Era

      • Audun Holme
      Pages 75-172

    6. Arabic Mathematics and Geometry

      • Audun Holme
      Pages 173-210

    7. The Geometry of Yesterday and Today

      • Audun Holme
      Pages 211-240

    8. Geometry and the Real World

      • Audun Holme
      Pages 241-249

  3. Introduction to Geometry

    1. Front Matter

      Pages 251-251
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    2. Axiomatic Geometry

      • Audun Holme
      Pages 253-263

    3. Axiomatic Projective Geometry

      • Audun Holme
      Pages 265-282

    4. Models for Non-Euclidian Geometry

      • Audun Holme
      Pages 283-298

    5. Making Things Precise

      • Audun Holme
      Pages 299-311

    6. Projective Space

      • Audun Holme
      Pages 313-323

    7. Geometry in the Affine and the Projective Plane

      • Audun Holme
      Pages 325-350

    8. Algebraic Curves of Higher Degrees in the Affine Plane \(\mathbb{R}^2\)

      • Audun Holme
      Pages 351-366

    9. Higher Geometry in the Projective Plane

      • Audun Holme
      Pages 367-396

    10. Sharpening the Sword of Algebra

      • Audun Holme
      Pages 397-412

    11. Constructions with Straightedge and Compass

      • Audun Holme
      Pages 413-433
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Keywords

About this book

This is a revised edition of the ?rst printing which appeared in 2002. The book is based on lectures at the University of Bergen, Norway.Over the years these lectures have covered many different aspects and facets of the wonderful ?eld of geometry. Consequently it has never been possible to give a full and ?nal account of geometry as such, at an undergraduatelevel: A carefully consideredselection has always been necessary. The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too oftenthe textsdealingwith geometrywhichgo intothe syllabusforteacher-students present the material in ways which appear pedantic and formalistic, suppressing the very powerful and dynamic character of this old ?eld, which at the same time so young. Geometry is a ?eld of mathematical insight, research, history and source of artistic inspiration. And not least important, an integral part of our common cultural heritage.

Reviews

From the reviews of the second edition:

“Devised primarily for future teachers of mathematics, but to be enjoyed by all lovers of geometry, including professional geometers, who will likely find something new in the historical part, this book renders an essential service to the mathematical community by presenting the story of geometry in two equal halves, the first half surveying its history up to Descartes and the second one presenting the version of geometry that emerged from the axiomatic revolution of the late 19th century, with an emphasis on algebraic geometry.” (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1202, 2011)

Authors and Affiliations

  • University of Bergen, Department of Mathematics, Bergen, Norway

    Audun Holme

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