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Geometric Origami

Geometric Origami

Front cover of Geometric Origami book

How do you fold regular polygons?

Can more be achieved by folding paper than by traditional ‘ruler and compass’ constructions?

Geometric Origami reveals some of the rich mathematics inherent in paper folding, and will help origamists, mathematicians and the interested general reader appreciate the value of studying the geometrical properties of folding a square of paper.

Part I of the book covers the mathematical theory of origami constructions.

Part II includes step-by-step folding instructions for fifteen regular polygons, from the equilateral triangle to the 19-gon.

Written by the mathematician and origamist Robert Geretschläger, Geometric Origami will appeal to:

A sample page from each chapter can be seen in the Book Gallery.

Reviews of Geometric Origami appear in

“This book is a delightful addition to a wonderful corner of mathematics where art and geometry meet in such a fruitful union.” Book Review

The author

Robert Geretschläger teaches mathematics at school and university in Graz, Austria.

His interest in origami goes back to childhood — fond memories of struggling to fold a frog without its legs turning to mush are still very present. A number of his published mathematical papers are somehow related to origami.

List of models

Folding polygons
  1. Maximum Equilateral Triangle
  2. Regular Triangular Grid
  3. Maximum Regular Octagon
  4. Maximum Regular 16-gon
  5. Maximum Regular Hexagon
  6. Maximum Regular Dodecagon
  7. Easy Regular Pentagon
  8. Maximum Regular Pentagon
  9. Maximum Regular Decagon
  10. Easy Regular Heptagon
  11. Maximum Regular Heptagon
  12. Regular Nonagon
  13. Regular Triskaidekagon
  14. Regular 17-Gon
  15. Regular 19-Gon


Part I    Some Theory

  1. Euclidean and Origami Procedures
    1. Geometric constructions and where they come from
    2. Elementary Euclidean procedures
    3. Elementary geometric procedures of origami
    4. Reducing Euclidean procedures to origami
    5. Reducing origami procedures to Euclidean constructions
  2. Origami Constructions and Algebra
    1. Linear equations
    2. Quadratic equations
    3. Folding cube roots
    4. Solving general cubic equations
    5. Trisecting angles
    6. Solving quartic equations
  3. Properties of Origami Constructions
    1. Dividing line segments into sections of equal length
    2. Six problems from one fold
    3. Determining common folding methods for given creases
    4. Origami constructions on a parabola
  4. The Maximum Polygon Problem

Part II    Some Practice

  1. Triangles, Squares and More
    1. Triangles
    2. The regular octagon and n-gons with n = 2k
    3. The regular hexagon and n-gons with n = 3 · 2k
  2. The Regular Pentagon and its Cousins
    1. Regular pentagons and the golden section
    2. Some precise folding methods
    3. The regular n-gon with n = 5 · 2k · 3l
  3. The Regular Heptagon Family
    1. The cubic equation
    2. The “easy” regular heptagon and the regular 14-gon
    3. The maximum regular heptagon
  4. A Few More Polygons
    1. The regular nonagon
    2. The regular triskaidekagon
    3. The regular 17-gon
    4. The regular 19-gon
On this page

Clicking a link will scroll the page to the relevant section.

Sample pages

Visit the Book Gallery to see a sample page from each chapter.

Book Gallery

“A well-written, beautifully illustrated reference work.” Book Review


Soft bound


17.0 cm by 24.6 cm


xiv + 198


Over 300 high quality black and white


978 0 9555477 1 3

“I would recommend this book as an enjoyable and informative read.” Book Review

Worldwide sales

Arbelos has delivered to customers in countries around the world:

  • Australia
  • Austria
  • Belgium
  • Brazil
  • Canada
  • China
  • Finland
  • France
  • Germany
  • Hong Kong
  • Hungary
  • Indonesia
  • Ireland
  • Israel
  • Kenya
  • Netherlands
  • New Zealand
  • Poland
  • Portugal
  • Qatar
  • Romania
  • South Africa
  • Switzerland
  • Thailand
  • Turkey
  • United Arab Emirates
  • United Kingdom
  • United States of America
Japanese version

Available in Japanese as “Mathematics of Origami”, published by Morikita Publishing:

Morikita Publishing