Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-10-06T09:48:53.765Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional theorems for schools

Published online by Cambridge University Press:  24 July 2023

Christopher Zeeman
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Geometry is gradually coming back into the school syllabus, but so far only 2-dimensional geometry. I would like to make a case for including some 3-dimensional geometry as well, because the latter is vital for describing the world throughout science, engineering and architecture. Higher-dimensional geometry also comprises a major part of modern research within mathematics itself. Also 3-dimensional geometry fosters both our intuitive understanding and our geometric imagination. It teaches us to see things in the round. It also trains us to see all sides of an argument simultaneously, as opposed to algebra and computing which emphasise thinking sequentially.

Type
Research Article
Information
The Mathematical Gazette , Volume 89 , Issue S1: Three-dimensional theorems for schools , March 2005 , pp. 1 - 92
Copyright
Copyright © The Mathematical Association 2005

References

Alberti, L B, Della pittura, Firenze, 1435.Google Scholar
Artin, E, Zur Isotopie zweidimensionaler Flchen im ℝ4, Abh. aus dem Math. Sem. Hamburg IV (1926) pp. 174-177.Google Scholar
Bool, F H, Ernst, B, Kist, J R, Locher, J L and Wierda, F, Escher: the complete graphic work, Thames and Hudson, 1992.Google Scholar
Courant, R and Robbins, H, What is mathematics?, OUP, 1941.Google Scholar
Coxeter, H S M, Interlocked rings of spheres, Scripta Mathematica, 18 (1952), pp. 113-121.Google Scholar
Coxeter, H S M, Introduction to geometry, Wiley, 1961.Google Scholar
Encyclopedia of World Art, McGraw-Hill, 1966, Plate 87.Google Scholar
Euclid: Elements, (trans. Heath, T L), 1908, Reprinted Dover, New York, 1956.Google Scholar
Fox, M, Chains, froths and a ten-bead necklace, Math. Gazette, 84 (July 2000) pp. 242-259.CrossRefGoogle Scholar
Hales, T C, A computer verification of the Kepler conjecture, Proc. Int. Congress of Math., Vol III, Beijing (2002) pp. 795-804.Google Scholar
Hilbert, D and Cohn-Vossen, S, Geometry and the imagination, AMS, Chelsea, 1952.Google Scholar
Jennings, G A, Modern geometry with applications, Springer, 1994.CrossRefGoogle Scholar
Klein, F, Lectures on the icosahedron, Kegan Paul, London, 1913.Google Scholar
Lickorish, W B R, An introduction to knot theory, Springer, 1997.CrossRefGoogle Scholar
Polydron International Ltd., Kemble, Cirencester, Glos. GL7 6BA.Google Scholar
Soddy, F, The hexlet, Nature, 138 (1936) p. 958 and 139 (1937) p. 154.CrossRefGoogle Scholar
Teaching and learning geometry 11-19, Report of a Royal Society and Joint Mathematical Council working group, 2001.Google Scholar
Zeeman, E C, Unknotting spheres in five dimensions, Bull. Amer. Math. Soc. 66 (1960) p. 198.CrossRefGoogle Scholar
Zeeman, E C, Geometry and perspective, Video and booklet, Royal Institution, London, 1987.Google Scholar
Zeeman, E C, Sudden changes in perception, Logos et Thorie des Catastrophes (ed. Petitot, J), Edition Patino, Geneva (1988) pp. 279-309.Google Scholar