What does a mathematician look like

Images of mathematics

A visual foray into mathematics
by Georg Glaeser and Konrad Polthier

What does a curve look like that completely fills the entire plane or space? Can you move a polyhedron flexibly, even turn it inside out? What is the projective plane or the four-dimensional space? Are there soap bubbles that are not the round ball? How can we better understand eddies and the complicated structure of flows?

In this book you will experience mathematics from its vivid side and find fascinating and previously unseen pictures that give you illustrative answers to all these questions. There are short explanatory texts, lots of literature references and lots of web links with further information for all pictures.

The book is for all friends of mathematics who don't just want to see dry text and endless formulas. From pupil to teacher, from student to professor. The pictures are intended to inspire and encourage you to deal with this or that topic that is supposedly only reserved for insiders. Get to know mathematics from a completely new and colorful side.

The book has now been published in softcover. For the printing of the softcover version, the 2nd extended edition has been fundamentally revised again:

  • extensively revised and corrected version softcover version,
    based on the 2nd edition with 8 additional double pages
  • A visual foray into mathematics
  • More than 1000 color images - aesthetic and clear
  • Informative and easy to understand text comments
  • Noteworthy and surprising things from arithmetic to topology


Enjoy the beauty and fascination of mathematics on more than 300 richly illustrated and commented pages on the topics:

  • Polyhedral models
  • Geometry in the plane
  • Problems old and new
  • Formulas and numbers
  • Functions and limits
  • Curves and knots
  • Geometry and topology of surfaces
  • Minimal surfaces and soap bubbles
  • Parquet and wraps
  • Spatial shapes and dimensions
  • Graphs and Incidences
  • Movable forms
  • Fractal sets
  • Maps and illustrations
  • Forms and processes in nature and technology

Reading samples

Extracts from the book for free download:

  • Table of Contents
  • Information flyer for the 1st edition
  • Reading samples:
    Johnson and Catalan bodies,
    The geometry of football,
    Celtic knots,
    The pseudosphere
    The Klein bottle
    The catenoid and its variations,
    Hamilton and Euler circles,
    The Pythagoras Tree,
    Möbius transformations from movements of the sphere,
    Area coloring and Riemann surfaces


  • Geometry, functions, numbers, topology, curves, surfaces, fractals, polyhedra
  • Entertainment math, popular science, brain teasers
  • Visualization


Images of mathematics
Georg Glaeser and Konrad Polthier

Published: 2. Erw. Edition in August 2010
15 chapters with 340 pages
over 1000 color images
Bound with dust jacket, EUR 34.95
ISBN: 978-3-8274-2565-2
Available from: Amazon and vismath

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