The changing shape of geometry : celebrating a century of geometry and geometry teaching / edited on behalf of the Mathematical Association by Chris Pritchard.
Guardat en:
| Publicat: |
Cambridge :
Cambridge University Press,
c2003.
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| Autor corporatiu: | |
| Altres autors: | |
| Col·lecció: | MAA spectrum
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| Matèries: | |
| Format: | Llibre |
Taula de continguts:
- General Introduction: Simplicity, Economy, Elegance / Chris Pritchard
- Pt. I. The Nature of Geometry
- 1.1. What is geometry? / G. H. Hardy
- 1.2. What is geometry? / Michael Atiyah
- Group A. Greek Geometry
- A1. Pythagoras' Theorem / Chris Denley
- A2. Angle at centre of a circle is twice angle at circumference / Charlie Stripp
- A3. Archimedes' theorem on the area of a parabolic segment / Tom Apostol
- A4. An isoperimetric theorem / John Hersee
- A5. Ptolemy's Theorem / Tony Crilly and Colin Fletcher
- Pt. II. The History of Geometry
- 2.1. Introductory Essay: A concise and selective history of geometry from Ur to Erlangen / Chris Pritchard
- 2.2. Greek geometry with special reference to infinitesimals / T. L. Heath
- 2.3. A straight line is the shortest distance between two points / J. H. Webb
- 2.4. On geometrical constructions by means of the compass / E. W. Hobson
- 2.5. What is a square root? A study of geometrical representation in different mathematical traditions / George Gheverghese Joseph
- 2.6. An old Chinese way of finding the volume of a sphere / T. Kiang
- 2.7. Mathematics and Islamic Art / Lesley Jones
- 2.8. Jamshid al-Kashi, calculating genius / Glen Van Brummelen
- 2.9. Geometry and Girard Desargues / B. A. Swinden
- 2.10. Henri Brocard and the geometry of the triangle / Laura Guggenbuhl
- 2.11. The development of geometrical methods / Gaston Darboux
- Group B. Elementary Euclidean Geometry
- B1. Varignon's Theorem / Chris Pritchard
- B2. Varignon's big sister? / Celia Hoyles
- B3. Mid-Edges Theorem / Toni Beardon
- B4. Van Schooten's Theorem / Doug French
- B5. Ceva's Theorem / Elmer Rees
- B6. Descartes Circle Theorem / H. S. M. Coxeter
- B7. Three Squares Theorem / Bill Richardson
- B8. Morley's Triangle Theorem / David Burghes
- Pt. III. Pythagoras' Theorem
- 3.1. Introductory Essay: Pythagoras' Theorem, A Measure of Gold / Janet Jagger
- 3.2. Pythagoras / Walter Rouse Ball
- 3.3. Perigal's dissection for the Theorem of Pythagoras / A. W. Siddons
- 3.4. Demonstration of Pythagoras' Theorem in three moves / Roger Baker
- 3.5. Pythagoras' Theorem / Jack Oliver
- 3.6. A neglected Pythagorean-like formula / Larry Hoehn
- 3.7. Pythagoras extended: a geometric approach to the cosine rule / Neil Bibby and Doug French
- 3.8. Pythagoras in higher dimensions, I / Lewis Hull
- 3.9. Pythagoras in higher dimensions, II / Hazel Perfect
- 3.10. Pythagoras inside out / Larry Hoehn
- 3.11. Geometry and the cosine rule / Colin Dixon
- 3.12. Bride's chair revisited / Roger Webster
- 3.13. Bride's chair revisited again! / Ian Warburton
- Group C. Advanced Euclidean Geometry
- C1. Desargues' Theorem / Douglas Quadling
- C2. Pascal's Hexagram Theorem / Martyn Cundy
- C3. Nine-point Circle / Adam McBride
- C4. Napoleon's Theorem and Doug-all's Theorem / Douglas Hofstadter
- C5. Miquel's Six Circle Theorem / Aad Goddijn
- C6. Eyeball Theorems / Antonio Gutierrez
- Pt. IV. The Golden Ratio
- 4.1. Introduction / Ron Knott
- 4.2. Regular pentagons and the Fibonacci Sequence / Doug French
- 4.3. Equilateral triangles and the golden ratio / J. F. Rigby
- 4.4. Regular pentagon construction / David Pagni
- 4.5. Discovering the golden section / Neville Reed
- 4.6. Making a golden rectangle by paper folding / George Markowsky
- 4.7. The golden section in mountain photography / David Chappell and Christine Straker
- 4.8. Another peek at the golden section / Paul Glaister
- 4.9. A note on the golden ratio / A. D. Rawlins
- 4.10. Balancing and golden rectangles / Nick Lord
- 4.11. Golden earrings / Paul Glaister
- 4.12. The pyramids, the golden section and 2[pi] / Tony Collyer and Alex Pathan
- 4.13. A supergolden rectangle / Tony Crilly
- Group D. Non-Euclidean Geometry & Topology
- D1. Four-and-a-half Colour Theorem / Derek Holton
- D2. Euler-Descartes Theorem / Tony Gardiner
- D3. Euler-Poincare Theorem / Carlo Sequin
- D4. Two Right Tromino theorems / Solomon Golomb
- D5. Sum of the angles of a spherical triangle / Christopher Zeeman
- Pt. V. Recreational Geometry
- 5.1. Introduction / Brian Bolt
- 5.2. The cube dissected into three yangma / James Brunton
- 5.3. Folded polyhedra / Cecily Nevill
- 5.4. The use of the pentagram in constructing the net for a regular dodecahedron / E. M. Bishop
- 5.5. Paper patterns: solid shapes from metric paper / William Gibbs
- 5.6. Replicating figures in the plane / Solomon Golomb
- 5.7. The sphinx task centre problem / Andy Martin
- 5.8. Ezt Rakd Ki: A Hungarian tangram / Jean Melrose
- 5.9. Dissecting a dodecagon / Doug French
- 5.10. A dissection puzzle / Jon Millington
- 5.11. Two squares from one / Brian Bolt
- 5.12. Half-squares, tessellations and quilting / Tony Orton
- 5.13. From tessellations to fractals / Tony Orton
- 5.14. Paper patterns with circles / William Gibbs
- 5.15. Tessellations with pentagons [with related correspondence] / J. A. Dunn
- 5.16. Universal games / Helen Morris
- Group E. Geometrical Physics
- E1. Euler's Identity / Keith Devlin
- E2. Clifford Parallels / Michael Atiyah
- E3. Tait Conjectures / Ruth Lawrence
- E4. Kelvin's Circulation Theorem / Keith Moffatt
- E5. Noether's Theorem / Leon Lederman and Chris Hill
- E6. Kepler's Packing Theorem / Simon Singh
- Pt. VI. The Teaching of Geometry
- 6.1. Introductory Essay: A century of school geometry teaching / Michael Price
- 6.2. The teaching of Euclid / Bertrand Russell
- 6.3. The Board of Education circular on the teaching of geometry / Charles Godfrey
- 6.4. The teaching of geometry in schools / C. V. Durell
- 6.5. Fifty years of change / A. W. Siddons
- 6.6. Milestone or millstone? / Geoffrey Howson
- 6.7. The place of geometry in a mathematical education / J. V. Armitage
- App. I. Report of the M. A. Committee on Geometry (1902)
- App. II. Euclidean Propositions.
