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Published online by Cambridge University Press: 15 September 2017
I ventured recently to recall to Professor Hadamard the fact that the asymptotes of any pencil of equilateral hyperbolas are also Simson lines of each triangle whose vertices are three base-points of the pencil. This provides an alternative approach to the generation of the hypocycloid treated in his paper in Math. Gazette, 29, 66-7, 1945.
Professor Hadamard thereupon sent me the following very concise proof of the identity of the asymptotes and Simpson lines and of the fact that they envelop a hypocycloid. He has now very kindly given me permission to communicate his letter to the Gazette
The two small footnotes have been inserted by me.
† These projections are on L, L', respectively, by definition of the Simpson lines.
‡ MM' and mm' being parallel diameters of the two circles.
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