<p>A chain suspended on two points hanging under gravity forms a curve called a <a href="https://en.m.wikipedia.org/wiki/Catenary" rel="noreferrer">Catenary</a>, 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:</p>
<p>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?</p>
<p>After all, non-parabolic mirrors seem to be frequently used as primary mirrors (and corrected by some secondary mirror).</p>

CC BY-SA 4.0
2022-08-22T09:26:34.613Z
similar: https://www.researchgate.net/publication/279514418_Shape_control_of_slack_space_reflectors_using_modulated_solar_pressure
planetmaker
CC BY-SA 4.0
2022-08-22T13:44:39.047Z
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...
uhoh
CC BY-SA 4.0
2022-08-22T16:57:07.810Z
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.
Ed V
CC BY-SA 4.0
2022-08-22T17:27:56.240Z
@uhoh yes!  bubble films FTW.   Not that I see that as a simple or stable mechanism.  Maybe some material which forms a bubble and then hardens to shape?  The problem with common bubbles (soap bubbles eg) is that the surface density is nonuniform as fluid "drains" to the lowest point.  We'll need a long-chain interlocked poly-something molecule!
Carl Witthoft
CC BY-SA 4.0
2022-08-23T03:30:06.507Z
Related: https://mathoverflow.net/q/69817
PM 2Ring
CC BY-SA 4.0
2022-08-23T06:32:04.897Z
@PM2Ring excellent find!
uhoh
CC BY-SA 4.0
2022-08-23T07:14:10.070Z
As Ed V & the mathoverflow post explain, your inextensible cloth isn't going to work. But FWIW, here's a rotated catenary. https://sagecell.sagemath.org/?z=eJxVkMFqwzAMhu-BvIPwLimY0qU7rAPDTrsNShnsGNxEbbwlkbGVrtnTz06yNfNBlu1f1vdLCAEHYs0IGsqwddoNoI_UMxj24Ie2RY5XV-PTBMJ6d4aDDo4D7F8hP5juDPkmz9ebx3W-TRMhRJqkybPpGJ0uOU0qPEGRefON6l6CbYgLS-HZq4eNhBZ9rd5cjxJKasgpcbetdtUOhQSyujQ8hLLY--R0i-pFNz5oK-0-5zKLzlss2Vz-XnXPVPS2Co6mq9XTRL8HBQ4v1PRsqCsizLbKSvK1hOwqIQBF0NV_zkUup39ghh3jDXTeZ1cxrOIwop5rbDF0F5FcgDmNFgADHIjGnGsWk9A6-ohuqIvqhbmxaHGea8lxTWenbW3K-Yv92tf0lU0DG6Oc-qsxykUPdUuDja4x3e_EfgB0QLAS&lang=sage
PM 2Ring
CC BY-SA 4.0
2022-08-24T01:44:10.070Z
Does "inextensible" automatically exclude *shear strains* as well? My coffee hasn't kicked in yet, I haven't been able to wrap my rigid head *conformally* around this problem yet :-)
uhoh
<telescope><mathematics><optics><mirror><mirror-making>
Would it be possible to create a telescope from a hanging reflective cloth?
2080
# Would it be possible to create a telescope from a hanging reflective cloth?

(Asked by: username_0 on 2022-08-22)

A chain suspended on two points hanging under gravity forms a curve called a [Catenary](https://en.m.wikipedia.org/wiki/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).

**Tags:** telescope, mathematics, optics, mirror, mirror-making
> **Comments:**
> **username_1**: similar: https://www.researchgate.net/publication/279514418_Shape_control_of_slack_space_reflectors_using_modulated_solar_pressure  
> **username_2**: 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...  
> **username_3**: 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.  
> **username_4**: @uhoh yes!  bubble films FTW.   Not that I see that as a simple or stable mechanism.  Maybe some material which forms a bubble and then hardens to shape?  The problem with common bubbles (soap bubbles eg) is that the surface density is nonuniform as fluid "drains" to the lowest point.  We'll need a long-chain interlocked poly-something molecule!  
> **username_5**: Related: https://mathoverflow.net/q/69817  
> **username_2**: @PM2Ring excellent find!  
> **username_5**: As Ed V & the mathoverflow post explain, your inextensible cloth isn't going to work. But FWIW, here's a rotated catenary. https://sagecell.sagemath.org/?z=eJxVkMFqwzAMhu-BvIPwLimY0qU7rAPDTrsNShnsGNxEbbwlkbGVrtnTz06yNfNBlu1f1vdLCAEHYs0IGsqwddoNoI_UMxj24Ie2RY5XV-PTBMJ6d4aDDo4D7F8hP5juDPkmz9ebx3W-TRMhRJqkybPpGJ0uOU0qPEGRefON6l6CbYgLS-HZq4eNhBZ9rd5cjxJKasgpcbetdtUOhQSyujQ8hLLY--R0i-pFNz5oK-0-5zKLzlss2Vz-XnXPVPS2Co6mq9XTRL8HBQ4v1PRsqCsizLbKSvK1hOwqIQBF0NV_zkUup39ghh3jDXTeZ1cxrOIwop5rbDF0F5FcgDmNFgADHIjGnGsWk9A6-ohuqIvqhbmxaHGea8lxTWenbW3K-Yv92tf0lU0DG6Oc-qsxykUPdUuDja4x3e_EfgB0QLAS&lang=sage  
> **username_2**: Does "inextensible" automatically exclude *shear strains* as well? My coffee hasn't kicked in yet, I haven't been able to wrap my rigid head *conformally* around this problem yet :-)  

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