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The ellipse and the five-centred arch

Published online by Cambridge University Press:  01 August 2016

Paul L. Rosin  and
Michael L.V. Pitteway
Paul L. Rosin
Affiliation:
Department of Computer Science, Cardiff University, PO Box 916, Cardiff CF24 3XF. emails: paul.Rosin@cs.cf.ac.uk, Milk.Pitteway@brunel.ac.uk
Michael L.V. Pitteway
Affiliation:
Department of Computer Science, Cardiff University, PO Box 916, Cardiff CF24 3XF. emails: paul.Rosin@cs.cf.ac.uk, Milk.Pitteway@brunel.ac.uk
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Extract

There has been a long history in the approximation of ellipses by circular arcs in order to simplify their construction and manipulation. Such approximation was of use for a wide variety of applications, in fields such as mathematics (generating figures), astronomy (analysing orbits), art (marking out large oval frames for ceiling painting), architecture (building masonry arches, floor plans, etc), and, more recently, the conversion of fonts from a general conic specification to circular arcs. Documented evidence goes as far back as the Italian Renaissance when various schemes were published by the architect Sebastiano Serlio in the sixteenth century. More contentiously, it has been argued that fifteen centuries previously the Romans used such approximations when designing and building their amphitheatres.

Type
Articles
Information
The Mathematical Gazette , Volume 85 , Issue 502 , March 2001 , pp. 13 - 24
Copyright
Copyright © The Mathematical Association 2001

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References

1. Hussain, F. and Pitteway, M. L. V., Rasterizing the outlines of fonts, Third International Conference on Raster Imaging and Digital Typography (1993) pp. 171–182.Google Scholar
2. Karow, P., Digital formats for typefaces, URW Verlag (1987).Google Scholar
3. Hart, V. and Hicks, P. (eds), Sebastiano Serlio on architecture : Books IV of ‘Tutte l’opère d’architettura et prospetiva’, Yale University Press (1996).Google Scholar
4. Golvin, J. C., L’amphitheatre Romain, Boccard (1988).Google Scholar
5. Thorn, A., Megalithic sites in Britain, Clarendon Press (1967).Google Scholar
6. Browning, H. C., The principles of architectural drawing, Watson-Guptill Publications (1996).Google Scholar
7. Rosin, P. L., A survey and comparison of traditional piecewise circular approximations to the ellipse, Computer Aided Geometric Design, 16 (4) (1999) pp. 269–286.CrossRefGoogle Scholar
8. Lockwood, E. H., Note 891, Math. Gaz. 14 (1928) pp. 136–137.Google Scholar
9. Lockwood, E. H., Length of ellipse, Math. Gaz. 16 (1932) pp. 269–270.Google Scholar
10. Lodge, A., Note 912, Math. Gaz. 14 (1928) p. 270.Google Scholar
11. Walker, A. W., Approximating to an ellipse by circular arcs, Math. Gaz. 38 (1954) p. 123.Google Scholar
12. Chaplin, T. K., Methods of constructing ellipses and parabolae, Math. Gaz. 29 (1945) pp. 12–14.CrossRefGoogle Scholar
13. Rosin, P. L., Analysing error of fit functions for ellipses, Pattern Recognition Letters 17 (14) (1996) pp. 1461–1470.Google Scholar
14. Almkkvist, G. and Berndt, B., Gauss, Landen, Ramanujan, the arithmetic mean, ellipses, π, and the Ladies Diary, The American Mathematical Monthly, 95 (1988) pp. 585–608.Google Scholar
15. Lockwood, E. H., A book of curves, Cambridge University Press (1961).Google Scholar