Timeline for Area of the minimal surface of a non-planar quadrilateral in 3d
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2018 at 0:07 | answer | added | Joseph O'Rourke | timeline score: 5 | |
| Nov 8, 2018 at 23:17 | comment | added | A876 | This was asked at math.stackexchange.com on Nov 7 2014.<br> This was migrated to mathoverflow.net (here) on Nov 20 2014.<br> A similar question was asked at math.stackexchange.com on Nov 30 2015.<br> That one generates the curve by simple linear interpolation between the 4 points, and doesn't say whether the result is "minimal".<br> Something like an answer was added on Nov 30 2015. (It is not an expression in terms of a, b, c, d.)<br> **Compute the area defined by four non-planar points**<br> math.stackexchange.com/questions/1552551/… | |
| Nov 20, 2014 at 4:40 | history | edited | François G. Dorais |
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| Nov 20, 2014 at 4:32 | history | migrated | from math.stackexchange.com (revisions) | ||
| Nov 9, 2014 at 19:00 | comment | added | Dirk | Regarding your other comment: I thought 'minimal surface' would mean 'surface of minimal area' but probably there are some local minima (whatever this means in this context)? | |
| Nov 9, 2014 at 18:54 | comment | added | Dirk | A formula in elliptic functions or another non-elementary integral would be OK. In the end I would be happy with a simple numerical method to calculate the value. | |
| Nov 9, 2014 at 17:13 | comment | added | Steven Stadnicki | Also, a caveat: you use the phrase 'a minimal surface' but it's not clear that there's a single minimal surface spanning the polygon and picking out the one of least area may not be trivial/formulaic. | |
| Nov 9, 2014 at 17:11 | comment | added | Steven Stadnicki | What sort of formula are you expecting for your answer? Given that (as you note) the surface is likely to be very complicated, your best-case scenario is probably going to be getting the result in terms of ratios of elliptic functions of cross-ratios or somesuch, but all of the examples I've seen solved explicitly (see the 'four lines' surface at people.fas.harvard.edu/~sfinch/csolve/ge.pdf , for instance) seem to take essential advantage of some of the symmetries of the example. | |
| Nov 7, 2014 at 14:28 | history | asked | Dirk | CC BY-SA 3.0 |