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Let's assume we have a, say, 10 cm * 20 cm, not very thick, rectangular object. We also have a huge ball, with a known radius of about 1 m. Now be put that rectangle onto the ball surface. What happens to the rectangle?

I know that a 2D-object doesn't fit very well onto a spherical surface, of course. Just wondering, does anyone know a way to get some numerical information about the distortion? I have googled A LOT but haven't really found anything.

I guess that a few great mathematicians have already solved this problem..?

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# A small rectangle on a large ball - distortion?

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