Is there any way to represent the surface of a sphere on a flat surface?

Question

I'm looking for a way to cover a giant sphere with cloth. My problem is that you can't just wrap the cloth aroung the sphere...because it will wrinkle uncontrollably. How can I make the cloth lay flat? I assume it means making many separate cuts that fit together in the shape of a sphere...but I can't figure it out yet. Please help!

Answer 1

Look at the Mercator projection of the earth.
It's effectively several triangles with 'curved edges'. that's about as near as you'll get. The more triangles the better the fit.
With cloth there's a good chance it will stretch in all the right places (!) so that it will fit. Paper would not.
RoyS

Answer 2

There is no way you are going to wrap a sphere with plane paper without wrinkles. May be you should check out the proof for finding the surface area of a sphere and also should remember that paper is a 2-D surface while sphere is a 3-D surface. You can only map points from one dimension to the other.

Answer 3

Practice cutting an orange into wedges, making sure to slice the orange through the "poles" or the navels of the orange. First slice is a diametrical cut from pole to pole. Now you have two halves. Cut these again into halves and so. Eat the orange and save the resulting peels. Perhaps cutting the cloth into similarly shaped "orange wedges" will give you what you need.

Also, look at a soccer ball. Notice that the soccer ball is covered with many flat shapes fitted together like a puzzle. I don't have a ball in front of me, but I think the shape is a hexagon.

Answer 4

The best way to approximate a sphere is still a variant on the icosahedron, a 20-faced polyhedron using equilateral triangles for each face.

Answer 5

try cutting small triangles and glue them on (small enough to lay flat) and you should be able to peice them together covering the whole sphere