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A chain suspended on two points hanging under gravity forms a curve called a Catenary, which can look pretty similar to a parabola. I'm not sure if this generalizes to the two dimensional case where an inextensible, flexible cloth is hanged from and within a circular rim, but assuming it does:

If that material were made to be reflective could it be used (possibly in combination with a secondary mirror (of which shape?)) as a telescope?

After all, non-parabolic mirrors seem to be frequently used as primary mirrors (and corrected by some secondary mirror).

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    $\begingroup$ similar: researchgate.net/publication/… $\endgroup$ Commented Aug 22, 2022 at 9:26
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    $\begingroup$ Interesting question! An initially flat fabric or film can't form a axially symmetric concave shape without elastic deformation, and the way woven fabrics from fibers, and continuous films will deform will e different. I'll bet there are engineering equations out there for the resulting shapes for "plates" deformed under gravity, but those will be small deviations, not "deep dish" shapes. Hmm... $\endgroup$
    – uhoh
    Commented Aug 22, 2022 at 13:44
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    $\begingroup$ How would you deal with seams? You can’t smoothly wrap a flat sheet (think paper map) around a hemisphere without making wrinkles or needing to cut and stitch, like in cartography. $\endgroup$
    – Ed V
    Commented Aug 22, 2022 at 16:57
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    $\begingroup$ Related: mathoverflow.net/q/69817 $\endgroup$
    – PM 2Ring
    Commented Aug 23, 2022 at 3:30
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    $\begingroup$ As Ed V & the mathoverflow post explain, your inextensible cloth isn't going to work. But FWIW, here's a rotated catenary. sagecell.sagemath.org/… $\endgroup$
    – PM 2Ring
    Commented Aug 23, 2022 at 7:14

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