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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. |
More information: |
Abstract:
Reviews
Publisher Synopsis
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 Read more...
WorldCat User Reviews (1)
Review from American Scientist
October 15, 2008
excerpt of review:
"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...
Read more...
October 15, 2008
excerpt of review:
"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 ways," mathematician <a href="http://www.stanwagon.com/">Stan Wagon</a> of <a href="http://www.macalester.edu/">Macalester College</a> wrote recently in <a href="http://www.americanscientist.org/">American Scientist</a>. "But nothing beats the construction of a physical model. And when the model conforms exactly to the mathematical prediction, it is very satisfying."
<a href="http://press.princeton.edu/titles/8624.html">How Round Is Your Circle? Where Engineering and Mathematics Meet</a> (Princeton University Press, 2008), by John Bryant and Chris Sangwin, is a satisfying guide to making such physical models. What singles out this applied geometry book, according to Wagon, is its emphasis on the relationship of model- and tool-building with the real world. Because the authors have actually made wood or metal models of most of the constructions they present, their words ring true.
Read the entire review at <a href="http://www.americanscientist.org/bookshelf/pub/applied-geometry">American Scientist</a>, October 2008.
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Related Subjects:(9)
- Engineering mathematics.
- Geometry, Plane.
- Geometry, Algebraic.
- Geometrical models.
- Géométrie plane.
- Géométrie algébrique.
- Modèles géométriques.
- inženirska matematika -- geometrija -- populariziranje znanosti.
- elementarna geometrija -- trigonometrija -- aplikacije -- fizika -- inženirske vede
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