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Napoleon revisited

Published online by Cambridge University Press:  03 November 2016

R. D. Nelson
R. D. Nelson*
Affiliation:
Ampleforth College, York
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Extract

If on the sides of a triangle ABC equilateral triangles are constructed, inwardly and outwardly, and their circumcircles drawn, the 6 circles will in general have 11 points of intersection: A, B, C; 2 points on each of the 3 sides; a point F common to the circumcircles of the outer triangles, and a point N common to those of the inner triangles (Fig. 1).

This article uses complex numbers to investigate the figure, and has as its main object the establishment of an extremal property of N.

Type
Research Article
Information
The Mathematical Gazette , Volume 58 , Issue 404 , June 1974 , pp. 108 - 116
Copyright
Copyright © Mathematical Association 1974

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References

1. Coxeter, H. S. M., Introduction to geometry. Wiley (1961).Google Scholar
2. Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited. Random House (1967).Google Scholar
3. Yaglom, I. M., Geometric transformations, Vols. I and II. Random House (1962 and 1968).Google Scholar
4. Courant, R. and Robbins, H., What is mathematics? Oxford University Press (New York, 1941).Google Scholar