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

Author: John Bryant; C J Sangwin
Publisher: Princeton : Princeton University Press, ©2008.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
'How Round is your Circle?' includes chapters on: hard lines; how to draw a straight line; four-bar variations; building the world's first rules; dividing the circle; falling aprat; follow my leader; all approximations are rational; all a matter of balance; and finding some equilibrium.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John Bryant; C J Sangwin
ISBN: 9780691131184 069113118X 9780691149929 0691149925
OCLC Number: 163625336
Description: xix, 306 p., [16] p. of plates : ill. (some col.) ; 25 cm.
Contents: Preface --
Acknowledgements --
ch. 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 --
ch. 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 --
ch. 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 mechanism --
ch. 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 --
ch. 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. ch. 6. Falling apart --
6.1. Adding up sequences of integers --
6.2. Duijvestijn's dissection --
6.3. Packing --
6.4. Plane dissections --
6.5. Ripping paper --
6.6. A homely dissection --
6.7. Something more solid --
ch. 7. Follow my leader --
ch. 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 --
ch. 9. All approximations are rational --
9.1. Laying pipes under a tiled floor --
9.2. Cogs and millwrights --
9.3. Cutting a metric screw --
9.4. The binary calendar --
9.5. The harmonograph--
9.6. A little nonsense! --
ch. 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 methods. ch. 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 Delamian's views on education --
ch. 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 --
12.5. Spiralling out of control --
12.6. Escaping from danger --
12.7. Leaning both ways! --
12.8. Self-righting stacks --
12.9. Two-tip polyhedra --
12.10. Uni-stable polyhedra --
ch. 13. Finding some equilibrium --
13.1. Rolling uphill --
13.2. Perpendicular rolling discs --
13.3. Ellipses --
13.4. Slotted ellipses --
13.5. The super-egg --
Epilogue --
References --
Index.
Responsibility: John Bryant and Chris Sangwin.
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Abstract:

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  Read more...

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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 Read more...

 
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Review from American Scientist

by deblenares (WorldCat user published 2008-10-15) Good Permalink
<h2 class="staticTitle">Book Review: How Round Is Your Circle?</h2>

October 15, 2008

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"The great power of computers to model various aspects of geometry and mechanics has made it possible to visualize things quickly and in useful and innovative...
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