Is there an object that meets this description?

Or a large sunhat?

Yup, and how geodesics look in curved spaces. That’s what the tape is for: Stick tape smoothly onto a curved surface, and it’ll follow a geodesic.

If you have a local glassmaker, you might be able to get an uncut bullion or bullseye.(They are used in making faux antique windows) Maybe it comes in a material that is safe for children to handle.

Maybe you can make one of these models. Guy said it cost him 20 bucks.

Ooh, the glass bullion looks perfect. It’s way too expensive, and I wouldn’t trust middle-schoolers not to drop it, but at least now I know what to call this thing if I make one out of plexiglass.

You are teaching this lesson to children? what age are they?
That sounds like advanced high-school geometry

Here is a plastic mold for making the halves for chocolate spheres. The bulge is a hemisphere, don’t know if that is too big for your purposes.

[QUOTE=Chronos

And I thought about papier-mache, but that probably wouldn’t take well to masking tape being repeatedly applied and pulled off.

Hence the mucilage, to provide protection and slide-ability. Epoxy would work too, and make the project even stronger.

I don’t know of any way to approach the problem that’s at the advanced high school level. You can do it with tensor calculus, which is college level, or you can do it by sticking tape on physical objects, which is accessible to kids. Take a strip of tape about as long as the width of the curved object, put it on starting at the edge of the object, and aim close to the bulge but a little off-center. Apply the tape smoothly, without wrinkling it, and it’ll follow a geodesic on the surface. After you’ve done this, take a look at the tape you’ve put on, and you’ll find that it bends around the bulge.

The actual activity would have a bit more build-up than this, involving flat maps and globes and stretched string and so on, but that’s the gist of it.

EDIT: Does “mucilage” have some specific meaning in a craft context? Looking online, it seems to just be a catch-all term for “gooey organic matter”.

Correction, the spandex was $20, the whole thing about $100.

Don Quixote’s helmet is a shaving basin.

Yes, it’s a kind of craft glue good for collages.

Update: I mentioned this to one of my colleagues, and he thinks that making these things would be a good project for his students. So we’re killing two birds with ein stein.

What about cymbals… as in musical, part of a drummers set…