© 2007

A Topological Picturebook


Table of contents

  1. Front Matter
    Pages i-xv
  2. George K. Francis
    Pages 1-13
  3. George K. Francis
    Pages 14-42
  4. George K. Francis
    Pages 43-64
  5. George K. Francis
    Pages 65-76
  6. George K. Francis
    Pages 77-98
  7. George K. Francis
    Pages 99-124
  8. George K. Francis
    Pages 125-148
  9. George K. Francis
    Pages 149-175
  10. George K. Francis
    Pages 176-179
  11. Back Matter
    Pages 180-194

About this book


Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what ``hands on'' really means.

- John Stillwell, University of San Francisco

The Topological Picturebook has taught a whole generation of mathematicians to draw, to see, and to think.

- Tony Robbin, artist and author of Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought

The classic reference for how to present topological information visually, full of amazing hand-drawn pictures of complicated surfaces.

- John Sullivan, Technische Universitat Berlin

A Topological Picturebook lets students see topology as the original discoverers conceived it: concrete and visual, free of the formalism that burdens conventional textbooks.

- Jeffrey Weeks, author of The Shape of Space

A Topological Picturebook is a visual feast for anyone concerned with mathematical images.  Francis provides exquisite examples to build one's "visualization muscles".  At the same time, he explains the underlying principles and design techniques for readers to create their own lucid drawings.

- George W. Hart, Stony Brook University

In this collection of narrative gems and intriguing hand-drawn pictures, George Francis demonstrates the chicken-and-egg relationship, in mathematics, of image and text. Since the book was first published, the case for pictures in mathematics has been won, and now it is time to reflect on their meaning. A Topological Picturebook remains indispensable.

- Marjorie Senechal, Smith College and co-editor of the Mathematical Intelligencer


Cisco Mathematica PostScript boundary element method design e-Book form group information intelligence techniques time topology university visualization

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • Book Title A Topological Picturebook
  • Authors George K. Francis
  • DOI
  • Copyright Information Springer-Verlag New York 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-96426-3
  • Softcover ISBN 978-0-387-34542-0
  • eBook ISBN 978-0-387-68120-7
  • Edition Number 1
  • Number of Pages XV, 194
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
  • Buy this book on publisher's site


From the reviews:

"I was very pleasantly surprised when I opened the book. … this is really a much richer book. Indeed, the approach it offers to drawing can have a significant impact on how we teach and think about mathematics. … If you are good at visualization and illustration, this book can help you become better yet. … this will give you concrete and specific suggestions for developing your skills. If you just appreciate skillful drawing and illustration, this book deserves a look." (William J. Satzer, MathDL, December, 2006)

"This book is a drawing manual for mathematicians. It is written by a great expert in the subject … . The author explained his techniques of drawing and of shading pictures, he explains when to use perspective and when not to use it, and so on. The numerous illustrations that are contained in this book as examples for drawing of mathematical objects are delightful … . This book is unique in the mathematical literature, and the present second printing is most welcome." (Athanase Papadopoulos, Zentralblatt MATH, Vol. 1105 (7), 2007)