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periodic
A conjecture on iterated circumcentres ★★
Author(s): Goddyn
Conjecture Let
be a sequence of points in
with the property that for every
, the points
are distinct, lie on a unique sphere, and further,
is the center of this sphere. If this sequence is periodic, must its period be
?
![$ p_1,p_2,p_3,\ldots $](/files/tex/76fdf443d711aba8f9bc175e273790c5d312ee79.png)
![$ {\mathbb R}^d $](/files/tex/b7b6e27766e9a15017888f33b0ae9c883f50af07.png)
![$ i \ge d+2 $](/files/tex/ecf80d79d3a60cfc0ef5f007c248c2744d235e25.png)
![$ p_{i-1}, p_{i-2}, \ldots p_{i-d-1} $](/files/tex/57f6002e7d08e5813e7d3b8a48f547a6903d3584.png)
![$ p_i $](/files/tex/ad57ca656a729070bb119d8bd17e370de0f3d913.png)
![$ 2d+4 $](/files/tex/adbc29137cd3501f8b9b51928cc54d6031083453.png)
Keywords: periodic; plane geometry; sequence
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