Timeline for A generalized ellipse
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2016 at 13:28 | comment | added | Ali Taghavi | @SebastianGoette Of course your very interesting comment can be counted as an independent answer, thanks a lot for that. | |
| Mar 8, 2016 at 17:18 | comment | added | Ali Taghavi | @DaveLRenfro thank you very much for your very interesting historical remark. | |
| Feb 9, 2016 at 20:12 | comment | added | Sebastian Goette | As explained in the paper cited in said MSE post, all $n$-ellipses are boundaries of compact and convex sets (though their algebraic closures aren't necessarily). The argument carries over to the case where you have any compactly supported finite measure $\mu$ on $\mathbb R^n$ and want to keep $f_\mu(z)=\int_{\mathbb R^n}|z-x|\,d\mu(x)$ constant. Simply regard $f_\mu$ along a straight line as a superposition of convex functions. Being the boundary of a compact convex set, the topology is clear (except for one degenerate case for each $\mu$ ...). | |
| Feb 9, 2016 at 19:41 | comment | added | Dave L Renfro | Interesting historical footnote: James Clerk Maxwell, On the description of oval curves, and those having a plurality of foci; with remarks by Professor Forbes, Proceedings of the Royal Society of Edinburgh 2 #28 (1845-466), 89-91. Forbes actually read the paper before the Royal Society of Edinburgh (on 6 April 1846) because Maxwell was not allowed due to his age. Maxwell was only 14 years old at the time. | |
| Feb 9, 2016 at 16:05 | history | edited | Ali Taghavi |
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| Feb 9, 2016 at 15:38 | comment | added | Ali Taghavi | @JosephO'Rourke Thank you very much for the link. | |
| Feb 9, 2016 at 15:35 | comment | added | Joseph O'Rourke | You might look at the $n$-ellipse, e.g., images at this MSE posting. | |
| Feb 9, 2016 at 15:20 | history | asked | Ali Taghavi | CC BY-SA 3.0 |