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The same decomposition works in higher dimensions. For NNN random points on a sphere, the probability they all lie in a hemisphere is also N/2N−1N / 2^{N-1}N/2N−1. The argument is identical: anchor a hemisphere at each point, observe that each event has probability 1/2N−11/2^{N-1}1/2N−1, and verify that at most one anchor can work (the complementary cap is at least a full hemisphere, so no other anchor's hemisphere can straddle it). TODO: If I figure out how to add 3d visualizations to this website, I'll cover the 3D case
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可以说,这是一台没有明显短板,基础很扎实的水桶机,而三星的回答,就是在参数卷进边际效应递减的死胡同、影像只剩下喜好而无客观差距的时代,在扎实的产品基础上,打造类似于隐私屏幕这样瞄准微小痛点,更聚焦、更人文的创新。
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