Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T09:04:11.753Z Has data issue: false hasContentIssue false
  • English
  • Français

On proving certain optimisation theorems in plane geometry

Published online by Cambridge University Press:  23 January 2015

I. Grattan-Guinness
I. Grattan-Guinness*
Affiliation:
Middlesex University Business School, The Burroughs, Hendon, London, NW4 4BT
Get access Rights & Permissions [Opens in a new window]

Extract

A pleasurable aspect of mathematics and its teaching is to review the diversity of ways in which theorems are proved. Especially in elementary branches, there are various kinds of proof: using (or avoiding) spatial geometry, analytic or coordinate geometry, common algebra, vectors, abstract algebras, matrices, determinants, the differential and integral calculus, and maybe mixtures thereof. Further, sometimes a proof of one kind is elegant while another is clumsy, or one proof of a theorem suggests why it follows while another proof is not perspicuous. There is also the question of whether a proof is direct or indirect (for example, proofby contradiction).

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 538 , March 2013 , pp. 75 - 80
Copyright
Copyright © The Mathematical Association 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Grattan-Guinness, I., Properties of inscribed and circumscribed rectangles, Math. Gaz. 96 (March 2012) pp. 71–77.CrossRefGoogle Scholar
2. Legendre, A. M., Eléments de géométric; avec des notes (12th edn.), Paris: Firmin Didot (1823). [1st edn. 1794, many later ones.]Google Scholar
3. Simon, M., Über die Entwicklung der Elementar-Geometrie im XIX Jahrhundert, Leipzig: Teubner (1906).Google Scholar
4. Zacharias, M., Elementargeometrie und elementare nicht-euklidische Geometrie in synthetischer Behandlung, in Encyklopädie der mathematischen Wissenschaften, vol. 3, pt. I, (1913) pp. 862–1172 (article IIIAB9).Google Scholar
5. Berkhan, G. and Meyer, W. F., Neuere Dreieckgeometrie, in Encyklopädie der mathematischen Wissenschafien, vol. 3, pt. I, (1914) pp. 1173–1276 (article IIIAB10).Google Scholar
6. G[abriel]-M[arie], F[rère], Exercices de géométrie: comprenant des méthodes géométriques et 2000 questions resolues (6th edn.) Tours: Marne et Fils; Paris: De Gigord (1920). [Repr. Paris: Gabay, 1991. Authorship conjectured.]Google Scholar
7. Russell, J. W., A sequel to elementary geometry with numerous examples (1st edn.), Oxford: Clarendon Press (1907).Google Scholar
8. Rouché, E. and Comberousse, C. de, Traité de géometrie (7th edn.), 2 vols., Paris: Gauthier-Villars (1900).Google Scholar