periodic


A conjecture on iterated circumcentres ★★

Author(s): Goddyn

\begin{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 $2d+4$? \end{conjecture}

Keywords: periodic; plane geometry; sequence

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