Intuitively, it seems like the closer the cap is to a full hemisphere, the less circle-like it would be but is that true? Could even caps that on, say, the globe of the Earth only extend to the Arctic Circle Be as uncircle-like as a cap that includes the equator? By this I mean, perhaps the amount you have to cut or deform a small cap is still the same percentage as a large cap?
2026-04-02 11:40:38.1775130038
Cap of a sphere: measure of how far from a circle it flattens to?
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No, it can never be the same percentage. Because if we analyze the data of arithmetic and geometry and find out that there is a difference between what you call a sphere and a hemisphere as a cap. If you have to say the same percentage as a thorn, you will mention it in the question, but if you have to know about a thorn in general, then it is a hemisphere. There is nothing more to worry about. You have the complete formula. Even if you have other information, you only need to consider the radius in mathematical practice. Knowing this radius will solve your question completely. We all know the area of a hemisphere and its formula for its size. 2πr² and ⅔πr³ respectively.
Regards, Puskar Sikdar!