Skip to main content
Home
plus.maths.org

Secondary menu

  • My list
  • About Plus
  • Sponsors
  • Subscribe
  • Contact Us
  • Log in
  • Main navigation

  • Home
  • Articles
  • Collections
  • Podcasts
  • Maths in a minute
  • Puzzles
  • Videos
  • Topics and tags
  • For

    • cat icon
      Curiosity
    • newspaper icon
      Media
    • graduation icon
      Education
    • briefcase icon
      Policy

      Popular topics and tags

      Shapes

      • Geometry
      • Vectors and matrices
      • Topology
      • Networks and graph theory
      • Fractals

      Numbers

      • Number theory
      • Arithmetic
      • Prime numbers
      • Fermat's last theorem
      • Cryptography

      Computing and information

      • Quantum computing
      • Complexity
      • Information theory
      • Artificial intelligence and machine learning
      • Algorithm

      Data and probability

      • Statistics
      • Probability and uncertainty
      • Randomness

      Abstract structures

      • Symmetry
      • Algebra and group theory
      • Vectors and matrices

      Physics

      • Fluid dynamics
      • Quantum physics
      • General relativity, gravity and black holes
      • Entropy and thermodynamics
      • String theory and quantum gravity

      Arts, humanities and sport

      • History and philosophy of mathematics
      • Art and Music
      • Language
      • Sport

      Logic, proof and strategy

      • Logic
      • Proof
      • Game theory

      Calculus and analysis

      • Differential equations
      • Calculus

      Towards applications

      • Mathematical modelling
      • Dynamical systems and Chaos

      Applications

      • Medicine and health
      • Epidemiology
      • Biology
      • Economics and finance
      • Engineering and architecture
      • Weather forecasting
      • Climate change

      Understanding of mathematics

      • Public understanding of mathematics
      • Education

      Get your maths quickly

      • Maths in a minute

      Main menu

    • Home
    • Articles
    • Collections
    • Podcasts
    • Maths in a minute
    • Puzzles
    • Videos
    • Topics and tags
    • Audiences

      • cat icon
        Curiosity
      • newspaper icon
        Media
      • graduation icon
        Education
      • briefcase icon
        Policy

      Secondary menu

    • My list
    • About Plus
    • Sponsors
    • Subscribe
    • Contact Us
    • Log in
    • 'How round is your circle?'

      1 June, 2008
      June 2008
      book cover

      How round is your circle? : Where engineering and mathematics meet

      John Bryant and Chris Sangwin

      In their new book John Bryant and Chris Sangwin explore the complex problems and challenges facing engineers and mathematicians now and throughout history. And these challenges don't have to come from complex questions. Take the simple problem of how to draw a straight line. The authors examine how to do this using linkages and other mechanical devices, and then ask how to divide an existing line into segments to create an accurate tool with which to measure other things. What this book excels at is taking seemingly simple problems such as these and thoroughly dissecting them down to the mathematical level.

      But it's not all theory. Many of the chapters invite the reader to get their hands dirty and actually build the devices, linkages and models detailed within. I think most readers will feel an urge to build a hatchet planimeter! A great deal can be done with the minimum of tools; sometimes pencil and paper suffice. For enthusiastic model makers with access to the right equipment, construction methods for many of the more complicated pieces are included. There is a good range of figures and illustrations, and more photos, videos, illustrations and interactivities are available on a supporting website.

      Bryant and Sangwin spend a lot of time looking at early attempts to draw straight lines, as well as an equally fundamental problem that has faced engineers though the ages: how to construct a mechanical linkage. We learn about James Watt's linkage from 1784, designed to constrain a straight line movement in an engine cylinder and then convert this into rotary output, and Peaucellier's linkage from 1864, which demonstrated, for the first time, that exact geometrical straight lines can be created from linkages. Many other uses of linkages are examined in detail, including the pantograph and creations such as Chebyshev's paradoxical mechanism.

      The difference between theory and practice — between constructing something using pure geometry and making a physical piece — is an important part of the book. Just how accurate you need to be to make something work, and the mathematics you need to check how accurate a tool is going to be, are shown in great detail. We learn, for example, how 50 pence pieces are not round, but do have constant width, and what tests not to use to prove it!

      This is a great book for engineers and mathematicians, as well as the interested lay person. Although some of the theoretical mathematics may not be familiar, you can skip it without losing the point. For school teachers and lecturers seeking to inspire, this is a fantastic resource.

      Book details:
      How round is your circle? : Where engineering and mathematics meet
      John Bryant and Chris Sangwin
      Hardback — 352 pages (2008)
      Princeton University Press
      ISBN-10: 069113118X
      ISBN-13: 978-0-691-13118-4

      About the author

      Owen Smith works for the Millennium Mathematics Project where he designs and develops beautiful websites, including Plus.

      • Log in or register to post comments

      Read more about...

      book review
      University of Cambridge logo

      Plus Magazine is part of the family of activities in the Millennium Mathematics Project.
      Copyright © 1997 - 2025. University of Cambridge. All rights reserved.

      Terms