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How Round Is Your Circle?: Where Engineering and Mathematics Meet [Paperback]

John Bryant , Chris Sangwin
4.7 out of 5 stars  See all reviews (12 customer reviews)

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Book Description

March 20, 2011 0691149925 978-0691149929

How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun.

John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

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How Round Is Your Circle?: Where Engineering and Mathematics Meet + The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)
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Editorial Reviews


"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.

Product Details

  • Paperback: 320 pages
  • Publisher: Princeton University Press (March 20, 2011)
  • Language: English
  • ISBN-10: 0691149925
  • ISBN-13: 978-0691149929
  • Product Dimensions: 0.8 x 6.1 x 9.2 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #601,685 in Books (See Top 100 in Books)

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Customer Reviews

4.7 out of 5 stars
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Most Helpful Customer Reviews
18 of 18 people found the following review helpful
5.0 out of 5 stars Modeling to illustrate mathematics June 22, 2008
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.
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13 of 13 people found the following review helpful
5.0 out of 5 stars Or how trisected is your Angle? May 18, 2008
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.
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10 of 11 people found the following review helpful
4.0 out of 5 stars Surprises, Ingenuity and ... a Few Disappointments August 18, 2008
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.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Original, informative hands-on book June 16, 2009
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!!
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1 of 1 people found the following review helpful
5.0 out of 5 stars amateur and professional engineers, LOOK! November 10, 2008
By reader
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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Format:Paperback|Verified Purchase
All I wanted to point out is you need the right device for the Kindle version. I have 3 devices with which to compare this book: Microsoft Surface 2 running Win 8.1 update 1 (10.6", 1920 x 1080, 208ppi), Nexus 10 (10.1" 2560×1600, 300ppi) and Nexus 7 2013 (7", 1920x1200, 323ppi) both running Android 4.4.2.

1. Text. The Windows 8.1 version of the Kindle app shows text in two columns in landscape, whereas on both Nexus the book is displayed in one column in landscape. Works fine on the smaller screen Nexus 7, harder to read on Nexus 10. No settings I can find to change this. In Portrait mode, they are all one column. The Nexus definitely have sharper looking text but both Nexus and Surface are readable.

2. Diagrams and formulas. This book depends heavily on illustrations and formulas for explanations. Unfortunately, those items do not scale on the Nexus device, i.e, no way to enlarge the diagrams or the formulas. On both Nexus, the diagrams got rendered way too small due to the high PPI. In fact, on both Nexus, the diagrams are exactly the same physical size. The rendered diagrams have labels of inside angles of triangles that are small so it very hard to read. On the Surface 2, it is sized appropriately (about 50% bigger measured physically), so even though the resolution of the device is lower, it is easier to read.

Moral of the story: High PPI <> readability. Whether this book should be a Kindle or physical book will depend on what device you have.
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