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How Round Is Your Circle?: Where Engineering and Mathematics Meet Paperback – 20 Mar 2011

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Product details

  • Paperback: 320 pages
  • Publisher: Princeton University Press (20 Mar 2011)
  • Language: English
  • ISBN-10: 0691149925
  • ISBN-13: 978-0691149929
  • Product Dimensions: 1.9 x 15.2 x 22.9 cm
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 118,786 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description


"There are many books that include ideas or instructions for making mathematical models. What is special about this one is the emphasis on the relation of model- or tool-building with the physical world. The authors have devoted themselves to making wood or metal models of most of the constructions presented; 33 color plates nicely show off their success in this area."--Stan Wagon, American Scientist

"The question posed by this book turns out to be a real toughie, but nevertheless the authors urge you to answer it. This gem of a book tackles several such questions, revealing why they are crucial to engineering and to our understanding of our everyday world. With a nice emphasis on practical experiments, the authors do a refreshing job of bringing out the mathematics you learned in school but sadly never knew why. And they show just how intuitive it can be."--Matthew Killeya, New Scientist

"Mathematics teachers and Sudoku addicts will simply be unable to put the book down. . . . Part magic show, part history lesson, and all about geometry, How Round Is Your Circle? is an eloquent testimonial to the authors' passion for numbers. Perhaps it will spark a similar interest in some young numerophile-to-be."--Civil Engineering

"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."--Owen Smith, Plus Magazine

"This book is very clearly written and beautifully illustrated, with line drawings and a collection of photographs of practical models. I can strongly recommend it to anyone with a bit of math knowledge and an interest in engineering problems--a terrific book."--Norman Billingham, Journal of the Society of Model and Experimental Engineers

"This book has many gems and rainbows. . . . The book will appeal to all recreational mathematicians . . . not just because of the way it is written, but also because of the way puzzles, plane dissections and packing and the odd paper folding or origami task are used to bring a point home. . . . More than one copy of this book should be in every school library. . . . It should help to inspire a new generation into mathematics or engineering as well as be accessible to the general reader to show how much mathematics has made the modern world."--John Sharp, LMS Newsletter

"This book can be dense, but it is great for dipping into, a rich resource of interesting thinking and project ideas. Bryant and Sangwin, the engineer and the mathematician, must have had a great time putting this book together. Their enthusiasm and humor shine through."--Tim Erickson, Mathematics Teacher

"The book is very nicely printed and contains many nice figures and photographs of physical models, as well as an extensive bibliography. It can be recommended as a formal or recreational lecture both for mathematicians and engineers."--EMS Newsletter

From the Inside Flap

"This book is a mine of exploration and information. I would recommend it to anyone with an interest in how things work and in how mathematics can help make sense of the world. Budding engineers and mathematicians will find it an inspiration."--John Mason, The Open University

"Truly impressive. This book builds a bridge across the ordinarily huge chasm separating how engineers and mathematicians view the world. Its innovative approach will be refreshing to readers with an engineering bent, and an eye-opener for many mathematicians. The audience for this book includes just about anyone who has any curiosity at all about how mathematics helps in explaining the world."--Paul J. Nahin, author of An Imaginary Tale

"I learned a lot from this book. I think it will have wide appeal, including with those readers who are interested in mathematics and those who are interested in building models. I was up until midnight the other night making a hatchet planimeter out of a coat hanger and washers!"--David Richeson, Dickinson College

--This text refers to an out of print or unavailable edition of this title.

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful By Mr. A. Clark on 9 July 2010
Format: Hardcover Verified Purchase
This book does what it claims and bridges the boundry between Mathematics and Enginering. It has some insights into how various linkages work, why rollers don't need to be round, how to make a ruler, how to draw a straight line and of course how round is your circle. The book looks at historical attempts to solve these problems and the various inventions that were produced along the way. Slide rules are explained in depth and if you've an old set of calipers with a vernier it explains how to use them.

For those who are more practical, many of the mechanisms can be made and there are photos in the centre section of the book

I bought this book specifically to learn more about the Peaucellier's linkage but found the other chapters facinating too.
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1 of 1 people found the following review helpful By Jose Rodolpho on 16 Mar 2014
Format: Paperback Verified Purchase
Being a mechanical engineer myself, I'm fascinated about geometry and its application on kinematics of mechanisms, which is what this book is specialized at. The examples are amazing and the book is a good option of entertainment, specially if you're after something different.
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1 of 1 people found the following review helpful By Rooster on 18 Mar 2013
Format: Paperback Verified Purchase
As an engineer, a lot of mathematics has been a bit of a mystery to me. As this book explains, in engineering there are no irrational numbers because engineers work in approximations. That is one of the biggest differences between engineering and mathematics, but the book also gives a big insight into some of the mathematical roots of engineering tools and techniques.

The chapter on planimeters was a bit hard going for me, but that's because I never did well at maths! There are a few sentences throughout the book that start "Clearly," or "Obviously," and what follows is far from that! But again, anyone with a reasonable level of maths won't have any problems.

There are also many interesting things to make, such as linkages and devices to demonstrate Pythagoras' Theorem. A very interesting and informative book and well worth reading by both mathematicians and engineers.
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By Andra 4ur on 2 Oct 2014
Format: Paperback Verified Purchase
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Most Helpful Customer Reviews on (beta) 14 reviews
18 of 18 people found the following review helpful
Modeling to illustrate mathematics 22 Jun 2008
By Bruce R. Gilson - Published on
Format: Hardcover
This book is in the tradition of the famous book "Mathematical Models," by H. Martyn Cundy and A. P. Rollett. It shows how to create models that illustrate particular mathematical laws, and in fact Cundy was consulted, while he was still alive, by the author. It is a worthy successor to Cundy & Rollett's book, concentrating mainly in two areas: linkages to draw straight lines and curves, and constant-breadth shapes, though entering a few other areas.

An example of the type of problem this book considers is: How would you construct "the first" protractor or ruler, if there were none already existing?

The spirit of the book is the kind of practical thinking that is thought of as engineering, but the mathematics discussed is fundamental. This is a highly recommended book.
13 of 13 people found the following review helpful
Or how trisected is your Angle? 18 May 2008
By R. H. Pratt - Published on
Format: Hardcover Verified Purchase
What this book shows you is that you can really understand Mathematics, when you try to build things, even something simple, like cutting a good circle from wood. Many areas of mathematics are discussed that people instinctively feel they understand, such as the roundness of a curve or circle, dividing an angle into 3 equal parts and other interesting Objects De Mathematica. You will find fascinating ways to really model the pythagorean theorem, or gather the sectors of a circle to make an equivalent triangle. There is much to discover between these pages, and Mathematics becomes concrete, objectified, and deeply understood. As another example: "what would a 3 dimensional object that has constant width throughout (based on the tetrahedron) Look like? You can see what this object looks like, when you read the work, and see the model. To add to your understanding, the Authors have constucted Models of the various mathematical principles and ideas, that you can see with your own eyes: such as "two-tip" polyhedrons, and summing the squares of numbers from 1 to n. Reading this book will improve your grasp of mathematics, as well as inspire you to study Engineering, if you havent already. Future Engineers, will be much smarter for having read this great book. Richard H. Pratt, Ph.D.
11 of 12 people found the following review helpful
Surprises, Ingenuity and ... a Few Disappointments 18 Aug 2008
By G. Poirier - Published on
Format: Hardcover
This fascinating book flags the spot where engineering and mathematics meet. Each chapter essentially covers a different subject: from linkages to vernier scales to slide rules to balancing dominoes to suspension bridges and so much more. The authors combine the rigidly theoretical approach of mathematics to the very real, practical and physical problems faced in engineering. The result is an amazing romp through various subject areas where the two meet. Very few mathematical derivations are presented here; instead, appropriate references are given throughout (but the reader may feel the urge to attempt some of the derivations him/herself). Some of the results are truly amazing, e.g., stacking a leaning tower of dominoes; some are very ingenious, e.g., the vernier scale and the slide rule; and some chapters I found rather disappointing, e.g., the chapter on suspension bridges - a subject dear to my heart that somehow I felt was lacking. The writing style can be a model of clarity for many chapters while, unfortunately, others seem rather cloudy by comparison; for example, I would place the first (Hard Lines) and seventh (Follow My Leader) chapters in the second category. But overall, the reader is bound to find this book very much worth the read. Those who are likely to relish this book the most would include mathematicians, engineers and serious science buffs. This book could also be used as a supplementary text for related university courses.
1 of 1 people found the following review helpful
Original, informative hands-on book 16 Jun 2009
By Nir Dahan - Published on
Format: Hardcover
I am an engineer interested in recreational mathematics so it is not surprising the book appealed to me. However, I believe the book will be more than just interesting for a wider technical oriented crowd.

I found the topics to be handled with extreme clarity. The examples are abundant and most important of all, the book just makes you want to put it down, jump out of the sofa to the nearest hardware store and build the models described, by yourself.
My favorite by far was the chapter on mechanical linkages.

One of my better purchases in a while!!
1 of 1 people found the following review helpful
amateur and professional engineers, LOOK! 10 Nov 2008
By reader - Published on
Format: Hardcover Verified Purchase
The review in American Scientist said it beautifully and also included a few of the gorgeous photos of demonstrations created by the two authors. There are blocks that can be piled up so they balance with their tops not over their bottoms. There is a planimeter made from a coat-hanger wire with which to find the area of a plane figure. There is a drill bit that can drill a square hole. Terrific fun at every level from the logo chief to the graduate engineer.
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