How round is your circle? : where engineering and mathematics meet / John Bryant and Chris Sangwin.

Includes bibliographical references (pages 297-302) and index.

Print version record.

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.

Cover; Title; Copyright; Contents; Preface; Acknowledgements; Chapter 1 Hard Lines; 1.1 Cutting Lines; 1.2 The Pythagorean Theorem; 1.3 Broad Lines; 1.4 Cutting Lines; 1.5 Trial by Trials; Chapter 2 How to Draw a Straight Line; 2.1 Approximate-Straight-Line Linkages; 2.2 Exact-Straight-Line Linkages; 2.3 Hart's Exact-Straight-Line Mechanism; 2.4 Guide Linkages; 2.5 Other Ways to Draw a Straight Line; Chapter 3 Four-Bar Variations; 3.1 Making Linkages; 3.2 The Pantograph; 3.3 The Crossed Parallelogram; 3.4 Four-Bar Linkages; 3.5 The Triple Generation Theorem; 3.6 How to Draw a Big Circle

3.7 Chebyshev's Paradoxical MechanismChapter 4 Building the World's First Ruler; 4.1 Standards of Length; 4.2 Dividing the Unit by Geometry; 4.3 Building the World's First Ruler; 4.4 Ruler Markings; 4.5 Reading Scales Accurately; 4.6 Similar Triangles and the Sector; Chapter 5 Dividing the Circle; 5.1 Units of Angular Measurement; 5.2 Constructing Base Angles via Polygons; 5.3 Constructing a Regular Pentagon; 5.4 Building the World's First Protractor; 5.5 Approximately Trisecting an Angle; 5.6 Trisecting an Angle by Other Means; 5.7 Trisection of an Arbitrary Angle; 5.8 Origami

Chapter 6 Falling Apart6.1 Adding Up Sequences of Integers; 6.2 Duijvestijn's Dissection; Colour Plates; 6.3 Packing; 6.4 Plane Dissections; 6.5 Ripping Paper; 6.6 A Homely Dissection; 6.7 Something More Solid; Chapter 7 Follow My Leader; Chapter 8 In Pursuit of Coat-Hangers; 8.1 What Is Area?; 8.2 Practical Measurement of Areas; 8.3 Areas Swept Out by a Line; 8.4 The Linear Planimeter; 8.5 The Polar Planimeter of Amsler; 8.6 The Hatchet Planimeter of Prytz; 8.7 The Return of the Bent Coat-Hanger; 8.8 Other Mathematical Integrators; Chapter 9 All Approximations Are Rational

9.1 Laying Pipes under a Tiled Floor9.2 Cogs and Millwrights; 9.3 Cutting a Metric Screw; 9.4 The Binary Calendar; 9.5 The Harmonograph; 9.6 A Little Nonsense!; Chapter 10 How Round Is Your Circle?; 10.1 Families of Shapes of Constant Width; 10.2 Other Shapes of Constant Width; 10.3 Three-Dimensional Shapes of Constant Width; 10.4 Applications; 10.5 Making Shapes of Constant Width; 10.6 Roundness; 10.7 The British Standard Summit Tests of BS3730; 10.8 Three-Point Tests; 10.9 Shapes via an Envelope of Lines; 10.10 Rotors of Triangles with Rational Angles; 10.11 Examples of Rotors of Triangles

10.12 Modern and Accurate Roundness MethodsChapter 11 Plenty of Slide Rule; 11.1 The Logarithmic Slide Rule; 11.2 The Invention of Slide Rules; 11.3 Other Calculations and Scales; 11.4 Circular and Cylindrical Slide Rules; 11.5 Slide Rules for Special Purposes; 11.6 The Magnameta Oil Tonnage Calculator; 11.7 Non-Logarithmic Slide Rules; 11.8 Nomograms; 11.9 Oughtred and Delamain's Views on Education; Chapter 12 All a Matter of Balance; 12.1 Stacking Up; 12.2 The Divergence of the Harmonic Series; 12.3 Building the Stack of Dominos; 12.4 The Leaning Pencil and Reaching the Stars

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