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gjm comments on Open thread, Jan. 18 - Jan. 24, 2016 - Less Wrong Discussion
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I can imagine it. You just have to embed it in a non-Euclidean geometry. A great circle can be constructed from 4 straight lines, and thus is a square, and it still has every point at a fixed distance from a common center (okay, 2 common centers), and thus is a circle.
The four straight lines in your construction don't meet at right angles.