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

    By: Bryant, John, 1934-Contributor(s): Sangwin, C. J. (Christopher J.)Material type: TextTextPublisher: Princeton : Princeton University Press, c2008Description: xix, 306 p., [16] p. of plates : ill. (some col.) ; 25 cmISBN: 9780691131184 (cloth : alk. paper); 069113118X (cloth : alk. paper)Subject(s): Engineering mathematics | Geometry, Plane | Geometry, Algebraic | Geometrical modelsDDC classification: 516/.15 LOC classification: QA484 | .B79 2008Online resources: Table of contents only
    Contents:
    Preface -- Acknowledgements -- Hard lines -- Cutting lines -- The Pythagorean theorem -- Broad lines -- Cutting lines -- Trial by trials -- How to draw a straight line -- Approximate-straight-line linkages -- Exact-straight-line linkages -- Hart's exact-straight-line mechanism -- Guide linkages -- Other ways to draw a straight line -- Four-bar variations -- Making linkages -- The pantograph -- The crossed parallelogram -- Four-bar linkages -- The triple generation theorem -- How to draw a big circle -- Chebyshev's paradoxical mechanism -- Building the world's first ruler -- Standards of length -- Dividing the unit by geometry -- Building the world's first ruler -- Ruler markings -- Reading scales accurately -- Similar triangles and the sector -- Dividing the circle -- Units of angular measurement -- Constructing base angles via polygons -- Constructing a regular pentagon -- Building the world's first protractor -- Approximately trisecting an angle -- Trisecting an angle by other means -- Trisection of an arbitrary angle -- Origami.
    Falling apart -- Adding up sequences of integers -- Duijvestijn's dissection -- Packing -- Plane dissections -- Ripping paper -- A homely dissection -- Something more solid -- Follow my leader -- In pursuit of coat-hangers -- What is area? -- Practical measurement of areas -- Areas swept out by a line -- The linear planimeter -- The polar planimeter of Amsler -- The hatchet planimeter of Prytz -- The return of the bent coat-hanger -- Other mathematical integrators -- All approximations are rational -- Laying pipes under a tiled floor -- Cogs and millwrights -- Cutting a metric screw -- The binary calendar -- The harmonograph-- A little nonsense! -- How round is your circle? -- Families of shapes of constant width -- Other shapes of constant width -- Three-dimensional shapes of constant width -- Applications -- Making shapes of constant width -- Roundness -- The British Standard Summit Tests of BS3730 -- Three-point tests -- Shapes via an envelope of lines -- Rotors of triangles with rational angles -- Examples of rotors of triangles -- Modern and accurate roundness methods.
    Plenty of slide rule -- The logarithmic slide rule -- The invention of slide rules -- Other calculations and scales -- Circular and cylindrical slide rules -- Slide rules for special purposes -- The magnameta oil tonnage calculator -- Non-logarithmic slide rules -- Nomograms -- Oughtred and Delamian's views on education -- All a matter of balance -- Stacking up -- The divergence of the harmonic series -- Building the stack of dominos -- The leaning pencil and reaching the stars -- Spiralling out of control -- Escaping from danger -- Leaning both ways! -- Self-righting stacks -- Two-tip polyhedra -- Uni-stable polyhedra -- Finding some equilibrium -- Rolling uphill -- Perpendicular rolling discs -- Ellipses -- Slotted ellipses -- The super-egg -- Epilogue -- References -- Index.
    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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    Item type Current library Call number Copy number Status Notes Date due Barcode
    Books Books Female Library
    		QA484 .B79 2008 (Browse shelf (Opens below)) 1 Available STACKS 51952000117704
    Books Books Main Library
    		QA484 .B79 2008 (Browse shelf (Opens below)) 1 Available STACKS 51952000144182

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

    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.

    '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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