How can I make a curved surface out of flat surfaces?

Question

I want to make several spherical things. For example, a half sphere made of iron, I have flat steel foils. Also a spherical parachute for model rocketry

How can I calculate the shape I have to cut the flat surface in order to get a spherical surface?

Answer 1

One way is to do reversed engineering.

Take an old plastic ball, cut it into two halves. Flatten one of the halves by making further straight cuts. You will realize that a series of triangles can be joined together to form a sphere.

You can also look at some projections of the globe for ideas.
http://www.hypermaths.org/quadibloc/maps/mcv0605.htm

Answer 2

you cant technically. Best way to get at it is a series of cut out triangles that you curve in the third dimension.

Answer 3

1. Make a cylinder of a sheet of paper.
2. Do a a sheet of paper in your pocket and press on it

Th