Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-07T22:31:51.026Z Has data issue: false hasContentIssue false
  • English
  • Français

1886. On the three-cusped hypocycloid—Addendum*

Published online by Cambridge University Press:  15 September 2017

J. Hadamard
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 30 , Issue 288 , February 1946 , pp. 48
Copyright
Copyright © Mathematical Association 1946 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

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.

References

† These projections are on L, L', respectively, by definition of the Simpson lines.

‡ MM' and mm' being parallel diameters of the two circles.