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Adventures in shape and space – and time

Published online by Cambridge University Press:  17 October 2018

Tom Roper
Tom Roper*
Affiliation:
10 Leyburn Avenue, Hipperholme, Halifax HX3 8NX e-mail: [email protected]
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Extract

As a youth entering the sixth form to study Mathematics, Further Mathematics and Physics I enjoyed the riches of the school's mathematics library and in particular three books which appealed to me, A mathematician's apology [1], A book of curves [2] and On growth and form [3].

Hardy's book [1] is one that an impressionable, young mathematician should not read unguided. It left me with the impression that the proper pursuit of mathematics was as a pure subject, of no use or application, to be studied for its own sake; to my regret, I held to this view for several years before finally being able to shake it off through teaching Newtonian mechanics. Looking across mathematics teaching today I seem to observe great interest in geometry, number and algebra ‘curiosities’ that are rooted entirely in mathematics. This in itself is no bad thing, since it clearly draws us and our students into the fascinating world of mathematics. But what of the applications of mathematics? Might they be equally fascinating? Surely we do not want to lure our students into Hardy's trap?

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 385 - 400
Copyright
Copyright © Mathematical Association 2018 

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References

1. Hardy, G. H., A mathematician's apology, Cambridge University Press (1992).Google Scholar
2. Lockwood, E. H., A book of curves, Cambridge University Press (1961).Google Scholar
3. Thompson, D'Arcy Wentworth, On growth and form, Cambridge University Press (1942).Google Scholar
4. Lim, Woong, Jeneva Clark, L. and Chauvot, Jennifer, Do you have the guts for ratios? Mathematics in School 46 (November 2017) pp. 3–7.Google Scholar
5. Haldane, J. B. S., On being the right size, (March 1926) Harper's Magazine available at www.phys.ufl.edu/courses/phy3221/spring10/HaldaneRightSize.pdfGoogle Scholar
6. Orton, A. and Roper, T., Science and mathematics: A relationship in need of counselling? Studies in Science Education, 35 No. 1 (2000) pp. 123–153.Google Scholar
7. AQA GCSE Biology Specification available at www.aqa.org.uk/subjects/sciences/gcse/biology-4401Google Scholar
8. Selkirk, Keith, Pattern and Place: An introduction to the mathematics of geography, Cambridge University Press (1982).Google Scholar
9. BBC, A giant penguin huddle – Earth's Seasonal Secrets: Winter Preview, available at https://www.youtube.com/watch?v=qwsle3pxgB8Google Scholar
10. Duncan, W. J., Physical similarity and dimensional analysis, Edward Arnold & Co. (1953).Google Scholar
11. McNeill Alexander, R., Animal mechanics (2nd edn.), Blackwell Scientific Publications (1983).Google Scholar
12. McNeill Alexander, R., The human machine, Natural History Museum Publications (1992).Google Scholar
13. Jean, Roger V., Phyllotaxis: A systematic study in plant morphogenesis, Cambridge University Press (1994).Google Scholar
14. Brousseau, A., On the trail of the California pine, Fibonacci Quarterly, 6(1) (1968) pp. 69–76.Google Scholar
15. Jean, R. V., Model testing in phyllotaxis, Journal of Theoretical Biology, 156(1) (1992) pp. 41–52.Google Scholar
16. Coxeter, H. S. M., Introduction to geometry (2nd edn.), John Wiley and Sons Inc. (1989).Google Scholar
17. Hofmeister, W., Allgemeine Morphologie des Gewachse, in Handbuch der Physiologischen Botanik, Vol. 1, Leipzig; Engelmann, pp. 405–664.Google Scholar
18. Atela, P., Golé, C. and Hotten, S., A dynamical system for plant pattern formation: a rigorous analysis, available at www.science.smith.edu/phyllo/Assets/pdf/talk.pdfGoogle Scholar
19. Hotten, Scott G., Symmetry of plants, a dissertation submitted in partial satisfaction of the requirements of the degree of Doctor of Philosophy in Mathematics at the University of California, Santa Cruz (December 1999).Google Scholar
20. Atela, P., Golé, C. and Hotten, S., A dynamical system for plant pattern formation: a rigorous analysis in Journal of Nonlinear Science, 12, pp. 641–676 (2002).Google Scholar
21. Douady, S. and Couder, Y., Phyllotaxis as a dynamical self-organising process: Part 1, The spiral modes resulting from time-periodic iterations in Journal of Theoretical Biology 178 (February 1996) pp. 255–274.Google Scholar
22. Douady, and Couder, , Magnetic Fluid Spiral (at Golden Angle/Fibonacci/1.618 no less) Experiment, available at https://www.youtube.com/watch?v=U-at-y3MicEGoogle Scholar