plane geometry

A conjecture on iterated circumcentres ★★

Author(s): Goddyn

Conjecture   Let $ p_1,p_2,p_3,\ldots $ be a sequence of points in $ {\mathbb R}^d $ with the property that for every $ i \ge d+2 $, the points $ p_{i-1}, p_{i-2}, \ldots p_{i-d-1} $ are distinct, lie on a unique sphere, and further, $ p_i $ is the center of this sphere. If this sequence is periodic, must its period be $ 2d+4 $?

Keywords: periodic; plane geometry; sequence

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