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  • Book
  • © 2017

Exploring Classical Greek Construction Problems with Interactive Geometry Software

Birkhäuser
  • 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
  • Includes supplementary material: sn.pub/extras

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

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Softcover Book USD 29.99 USD 49.99
40% discount Price excludes VAT (USA)
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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Ad Meskens, Paul Tytgat
    Pages 1-9
  3. The Genesis of Geometry

    • Ad Meskens, Paul Tytgat
    Pages 11-26
  4. Compass and straightedge constructions

    • Ad Meskens, Paul Tytgat
    Pages 27-41
  5. The Delian Problem

    • Ad Meskens, Paul Tytgat
    Pages 43-53
  6. Trisecting an angle

    • Ad Meskens, Paul Tytgat
    Pages 55-74
  7. Squaring the circle

    • Ad Meskens, Paul Tytgat
    Pages 75-104
  8. Constructible numbers

    • Ad Meskens, Paul Tytgat
    Pages 105-119
  9. The Cinderella of regular polygons

    • Ad Meskens, Paul Tytgat
    Pages 121-126
  10. Back Matter

    Pages 127-185

About this book

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS 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.


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)

Authors and Affiliations

  • Department of Education and Training, Artesis Plantijn University College Department of Education and Training, Antwerpen, Belgium

    Ad Meskens

  • Antwerpen, Belgium

    Paul Tytgat

Bibliographic Information

  • Book Title: Exploring Classical Greek Construction Problems with Interactive Geometry Software

  • Authors: Ad Meskens, Paul Tytgat

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-42863-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2017

  • Softcover ISBN: 978-3-319-42862-8Published: 17 February 2017

  • eBook ISBN: 978-3-319-42863-5Published: 02 February 2017

  • 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 it now

Buying options

eBook USD 19.99 USD 39.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 29.99 USD 49.99
40% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access