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Geometric Constructions

  • George E. Martin

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. George E. Martin
    Pages 1-28
  3. George E. Martin
    Pages 29-51
  4. George E. Martin
    Pages 53-68
  5. George E. Martin
    Pages 69-82
  6. George E. Martin
    Pages 83-96
  7. George E. Martin
    Pages 97-105
  8. George E. Martin
    Pages 107-108
  9. George E. Martin
    Pages 109-121
  10. George E. Martin
    Pages 123-144
  11. George E. Martin
    Pages 145-159
  12. Back Matter
    Pages 189-206

About this book

Introduction

Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations. As specified by Plato, the game is played with a ruler and compass. The first chapter is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never seen. The second chapter formalizes Plato's game and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, using only a compass, using toothpicks, using a ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort. This is as much an algebra book as it is a geometry book. Since all the algebra and all the geometry that are needed is developed within the text, very little mathematical background is required to read this book. This text has been class tested for several semesters with a master's level class for secondary teachers.

Keywords

Mathematica Scratch algebra boundary element method class construction form geometry history of mathematics mathematics philosophy real number story theorem tool

Authors and affiliations

  • George E. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0629-3
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6845-1
  • Online ISBN 978-1-4612-0629-3
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site