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© 2017

Exploring Classical Greek Construction Problems with Interactive Geometry Software

  • This book is the first to apply Interactive Geometry Software to classic Greek construction problems in a didactical, enquiry based approach

  • The history of classic Greek construction problems explored with IGS

  • An exciting enquiry based and novel approach to Greek construction problems

  • While designed as enrichment material for classroom use it will appeal to anyone curious about the classic Greek construction problems

Book

Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Ad Meskens, Paul Tytgat
    Pages 1-9
  3. Ad Meskens, Paul Tytgat
    Pages 11-26
  4. Ad Meskens, Paul Tytgat
    Pages 27-41
  5. Ad Meskens, Paul Tytgat
    Pages 43-53
  6. Ad Meskens, Paul Tytgat
    Pages 55-74
  7. Ad Meskens, Paul Tytgat
    Pages 75-104
  8. Ad Meskens, Paul Tytgat
    Pages 105-119
  9. Ad Meskens, Paul Tytgat
    Pages 121-126
  10. Back Matter
    Pages 127-185

About this book

Introduction

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software. The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of GeoGebra the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves.

By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

Keywords

Delian problem straightedge and compass ruler and compass GeoGebra neusis circle quadrature duplication of the cube doubling the cube trisection interactive geometry enquiry based learning heptagon Euclid

Authors and affiliations

  1. 1.Department of Education and TrainingArtesis Plantijn University College Department of Education and TrainingAntwerpenBelgium
  2. 2.AntwerpenBelgium

Bibliographic information

  • Book Title Exploring Classical Greek Construction Problems with Interactive Geometry Software
  • Authors Ad Meskens
    Paul Tytgat
  • Series Title Compact Textbooks in Mathematics
  • Series Abbreviated Title Compact Textbooks in Mathematics
  • DOI https://doi.org/10.1007/978-3-319-42863-5
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-42862-8
  • eBook ISBN 978-3-319-42863-5
  • Series ISSN 2296-4568
  • Series E-ISSN 2296-455X
  • Edition Number 1
  • Number of Pages XII, 185
  • Number of Illustrations 150 b/w illustrations, 10 illustrations in colour
  • Topics Geometry
    History of Mathematical Sciences
    Mathematics Education
  • Buy this book on publisher's site

Reviews

“This book provides historical sketches to accompany the problems. This places the activity in context, and will motivate some students to look more closely at the culture and history of mathematics. I thoroughly enjoyed the opportunity to review this book, and recommend it to anyone interested in this area of mathematics. … The book is clearly written while remaining brief and is excellently illustrated. The exercises are interesting and in my view well-judged for undergraduate students.” (Chris Sangwin, International Journal of Research in Undergraduate Mathematics Education, Vol. 4, 2018)