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Kürschak’s tile

Published online by Cambridge University Press:  22 September 2016

G. L. Alexanderson  and
Kenneth Seydel
G. L. Alexanderson
Affiliation:
University of Santa Clara, Santa Clara California 95053, USA
Kenneth Seydel
Affiliation:
Skyline College, San Bruno, California 94066, USA
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Extract

Why is such a nice result rarely, if ever, found in texts? Perhaps because it is usually necessary to use trigonometry to calculate the areas of regular polygons. A regular n-gon inscribed in a unit circle has an area n times that of the isosceles triangle having an edge as base and the centre as apex; that is,

area of regular n-gon = n × (1/2. 1.1. sin (360/n)°) = 1/2n sin (360/n)°.

Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 421 , October 1978 , pp. 192 - 196
Copyright
Copyright © Mathematical Association 1978

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References

1. Pólya, G. and Szegö, G., Problems and theorems in analysis, Vol. 2. Springer-Verlag (1976).Google Scholar
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3. Boltyanskii, V. G., Equivalent and equidecomposable figures. Heath, D. C. (1963).Google Scholar
4. Ball, W. W. Rouse and Coxeter, H. S. M., Mathematical recreations and essays (11th edition). Macmillan (1939).Google Scholar
5. Schoenberg, I. J., Approximating lengths, areas and volumes by polygons and polyhedra, Delta 7, 32–6 (1977).Google Scholar