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Make a square, split each side into two halves, producing four cells. Put a circle into each cell such that it fills it completely. There is a small gap right in the middle of the square. Put a circle there again such that it touches the other four circles. The central circle is obviously inside the square, right? Yes, but only if the dimension you are in is $D\le9$. Above that, the central cicle actually spills out from the cube, despite the $2^D$ spheres in their cells keeping it in. In this post I present this simple-to-compute yet utterly counter-intuitive result.

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Yuanzhao Zhang ,Stevenh Strogatz , ,

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