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Anamorphoscopes another look at circle inverting mirrors

Published online by Cambridge University Press:  23 January 2015

John Sharp,
B. G. Nickel and
J. L. Hunt
John Sharp
Affiliation:
London Knowledge Laboratory, Institute of Education, 23-29 Emerald Street, London WC1 3QS, e-mail: sliceforms@yahoo.co.uk
B. G. Nickel
Affiliation:
Department of Physics, University of Guelph, Guelph ON N1G 2W1, Canada, e-mails: phyjlh@physics.uoguelph.ca; bgn@physics.uoguelph.ca
J. L. Hunt
Affiliation:
Department of Physics, University of Guelph, Guelph ON N1G 2W1, Canada, e-mails: phyjlh@physics.uoguelph.ca; bgn@physics.uoguelph.ca
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Extract

In 1979 Philip W. Kuchel published a paper [1] in the Mathematical Gazette on using curved mirrors as a means of demonstrating the transformation known as inversion in a circle. He called the mirrors ‘anamorphoscopes’ since he came to the idea as a special case of the conical mirror anamorphosis which was a popular optical toy from the seventeenth century onwards [2]. In this paper we revisit his ideas with current technology and provide some extensions to Kuchel's derivation.

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Type
Articles
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The Mathematical Gazette , Volume 95 , Issue 532 , March 2011, pp. 1 - 16
Copyright
Copyright © The Mathematical Association 2011

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References

1. Kuchel, Philip W., Anamorphoscopes: a visual aid for circle inversion, Math. Gaz. 63 (June 1979), pp. 82–89.Google Scholar
2. Baltrušaitis, Jurgis (translated by Strachan, W. J.), Anamorphic Art, Abrams, New York (1977).Google Scholar
3. Hunt, J. L., Nickel, B. G., Gigault, Christian, Anamorphic Images, Amer. Journal of Physics 68 (2000) pp. 232–237.CrossRefGoogle Scholar
4. Cargo, Gerald T., Graver, Jack E., Troutman, John L., Designing a mirror that inverts in a circle, Mathematical Intelligencer, 24, pp. 4–8.Google Scholar
5. Abramowitz, and Stegun, , Handbook of Mathematical Functions Dover, New York (1970).Google Scholar
6. Kempe, A. B., How to draw a straight line: A lecture on Linkages, London (1877).Google Scholar
7. POV-Ray is available from www.povray.org Google Scholar