Timeline for Equations for an algebraic gömböc
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2022 at 15:00 | history | edited | YCor |
edited tags
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| Jul 3, 2022 at 14:05 | history | edited | LSpice | CC BY-SA 4.0 |
While this is on the front page, fix hyphens, and link to @Stopple's comment
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| Jul 3, 2022 at 13:23 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Apr 7, 2011 at 9:03 | comment | added | Roland Bacher | After reflexion, I think algebraic gömböcs exist if there exist gömböcs whose two equilibrium positions correspond to points are sufficiently differentiable with strictly positive scalar curvature, then one can find algebraic surfaces which match such gömböcs up to sufficiently high order (I guess order 2 should be enough) and which are close enough elsewhere. I have the impression that the gömböcs given in the proof by Domokos and Varkonyi satisfy these conditions (they are very tiny perturbations of spheres). The problem of convexity is however left and has also to be solved. | |
| Apr 7, 2011 at 6:28 | comment | added | Daniel Litt | Semi-algebraic sets, are, however, doable, as I remark in my answer. | |
| Apr 7, 2011 at 6:24 | history | edited | Roland Bacher | CC BY-SA 2.5 |
deleted 4 characters in body; added 124 characters in body
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| Apr 7, 2011 at 6:22 | comment | added | Roland Bacher | I agree that this is not obvious. The boundary of a gömböc can of course be approximated arbitrarily well by an algebraic surface but it is not obvious that such a surface defines a body which is convex. Moreover, small perturbation might create additional equilibria as shown in the paper of Domokos and Varkonyi. I should definitively have asked for existence! | |
| Apr 7, 2011 at 0:34 | answer | added | Daniel Litt | timeline score: 8 | |
| Apr 6, 2011 at 23:11 | comment | added | Stopple | I don't mean to sound argumentative, but I don't see why there are algebraic solutions. Neither wikipedia, nor the Math Intelligencer article wikipedia references, refer to any. | |
| Apr 6, 2011 at 19:06 | comment | added | Roland Bacher | Thank you, Anton. Concerning Stopple's comment, I do not see any contradiction: tiny can be very tiny! | |
| Apr 6, 2011 at 19:05 | history | edited | Roland Bacher | CC BY-SA 2.5 |
deleted 16 characters in body; edited title
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| Apr 6, 2011 at 18:56 | comment | added | Stopple | Where you claim "Such a convex body keeps its properties under tiny perturbations", the wikipedia page actually seems to say the opposite: "The shape of those bodies is very sensitive to small variation." So why should there be any algebraic solutions? | |
| Apr 6, 2011 at 18:09 | history | asked | Roland Bacher | CC BY-SA 2.5 |