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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
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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).

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

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References

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