I am not a mathematician and I was up till the early hours of this morning trying to solve the problem of building a sphere from circular panels which are sections of a sphere. I did not succeed and am appealing for help.
My raw-material is circular slices of a sphere . I don't know what the mathematical term for these is but they are essentially saucers created by the taking a slice off a sphere.
If the diameter of the sphere is 100 then the diameter out of my saucers is 50; the radius of curvature of the saucers is of course 50. From each saucer I will cut a rectangular panel and I then wish to glue these panels together to create my sphere
There is an additional complicating factor - I don't actually wish to create a complete sphere but a sphere with a slice taken off it. If I stand this mutilated sphere on a flat surface with the open end downwards the height of the assembly is to be 90.
I wish to use the minimum number of panels with the minimum number of different panels sizes and of course I also need to determine what these panels sizes should be. I am hoping that it will be possible to do it with two or three different panels sizes.
I am hoping that my description of the problem is sufficiently comprehensible to allow some kind soul to take pity on me and tell me what to do.