Timeline for Application for functions of the shape $r = f(\theta)$
Current License: CC BY-SA 3.0
5 events
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| Dec 29, 2022 at 20:04 | comment | added | LSpice | The arXiv preprint referenced by @terceira: Cooper - On the relevance of the differential expressions $f^2 + f'^2$, $f + f''$ and $f f'' - f'^2$ for the geometrical and mechanical properties of curves. Thanks! | |
| Dec 29, 2022 at 6:04 | comment | added | terceira | @LSpice The mathematician in question was from the Gaeltacht so that his name was gaelic. At that time the system of transliterating names into english was in flux, in particular with respect to the patronymic prefix and during his lifetime more than one version was used for his surname. By the way, if you are interested in his spirals and the related catenaries, you can find material in the arxiv preprint 1102.1579. The decisive fact is that the $f$ which arises has the property that $f+f''$ is proportional to a power of $f$. | |
| May 12, 2021 at 15:19 | comment | added | LSpice | @user6891, is that Maclaurin, or a different Scottish mathematician? I cannot easily find a description of McLaurin or Maclaurin spirals. | |
| Dec 21, 2013 at 22:23 | comment | added | user6891 | Since you mention spirals, a really remarkable family of these are the so-called McLaurin spirals which were discovered by this Scottish mathematcian in the 18 th century. They are those with $f$ of the form $(\cos(n \theta))^{\frac 1n}$ and have a plethora of remarkable properties, e.g., they are all orbits for power laws. The logarithmic spiral is a (degenerate) special case. They are also catenaries for such laws. | |
| Dec 21, 2013 at 21:39 | history | answered | Victor Protsak | CC BY-SA 3.0 |