Timeline for Is the developable surface between two conic sections, not in the same plane, algebraic?
Current License: CC BY-SA 4.0
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| Jan 23, 2021 at 23:46 | comment | added | Jap88 | This was a question related to a stack-exchange question. For some applied algebraic geometry and a partial answer to this question, see: math.stackexchange.com/questions/3974536/… | |
| Jan 16, 2021 at 22:08 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 21:41 | comment | added | Jap88 | @JosephO'Rourke Thanks. I have read some of Sturmfels work before. So, a question then is if a tangent developable of this kind is always algebraic? I will read the article. | |
| Jan 16, 2021 at 20:47 | comment | added | Joseph O'Rourke | You might look at this paper: Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). "The edge surface is in general the tangent developable of a curve." "The union of all stationary bisecant lines is the edge surface of the curve." | |
| Jan 16, 2021 at 20:35 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 20:26 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 20:24 | comment | added | Jap88 | @WillSawin thanks. I understand the comment by MoisheKohan. It wasn't clear. I have tried to clarify. Convex hull was not the correct term here. | |
| Jan 16, 2021 at 20:21 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 20:15 | comment | added | Will Sawin | @Jap88 Is a cylinder, viewed as the convex hull of two circles in two planes, an example of what you mean? Then I guess you want to take the boundary of the convex hull, less any components contained in the planes. Such a set will always be semialgebraic, at least - defined by polynomial equations and inequalities. One proof of this is to use the quantifier elimination for real closed fields, but that's a bit of a sledgehammer. | |
| Jan 16, 2021 at 20:11 | comment | added | Will Sawin | @MoisheKohan I think an asker, especially a new user, deserves more chances to clarify their question than that. | |
| Jan 16, 2021 at 20:03 | review | Close votes | |||
| Jan 19, 2021 at 20:26 | |||||
| Jan 16, 2021 at 19:38 | comment | added | Moishe Kohan | Keep in mind that such convex hull will be always 3-dimensional. If you mean the boundary of this convex hull, then it will never be developable. Voting to close as unclear. | |
| Jan 16, 2021 at 18:32 | comment | added | Jap88 | Thanks. The question was not right. I reformulated. I might go over to stack exchange instead. | |
| Jan 16, 2021 at 18:31 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 18:07 | comment | added | Moishe Kohan | Consider the graph of the function $f(x,y)=e^x$. Your question is more appropriate for math stack exchange. | |
| Jan 16, 2021 at 17:58 | history | edited | Jap88 | CC BY-SA 4.0 |
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| Jan 16, 2021 at 17:57 | review | First posts | |||
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| Jan 16, 2021 at 17:51 | history | asked | Jap88 | CC BY-SA 4.0 |