http://openproblemgarden.org/op/a_conjecture_on_iterated_circumcentres Comments for "A conjecture on iterated circumcentres" en http://openproblemgarden.org/op/a_conjecture_on_iterated_circumcentres <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/goddyn">Goddyn</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/geometry">Geometry</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/76fdf443d711aba8f9bc175e273790c5d312ee79.png" alt="$ p_1,p_2,p_3,\ldots $" /> be a sequence of points in <img class="teximage" src="/files/tex/b7b6e27766e9a15017888f33b0ae9c883f50af07.png" alt="$ {\mathbb R}^d $" /> with the property that for every <img class="teximage" src="/files/tex/ecf80d79d3a60cfc0ef5f007c248c2744d235e25.png" alt="$ i \ge d+2 $" />, the points <img class="teximage" src="/files/tex/57f6002e7d08e5813e7d3b8a48f547a6903d3584.png" alt="$ p_{i-1}, p_{i-2}, \ldots p_{i-d-1} $" /> are distinct, lie on a unique sphere, and further, <img class="teximage" src="/files/tex/ad57ca656a729070bb119d8bd17e370de0f3d913.png" alt="$ p_i $" /> is the center of this sphere. If this sequence is periodic, must its period be <img class="teximage" src="/files/tex/adbc29137cd3501f8b9b51928cc54d6031083453.png" alt="$ 2d+4 $" />? </div> </tr></td> </table> </td> </tr> </table> Goddyn, Luis A. periodic plane geometry sequence Geometry http://openproblemgarden.org/op/a_conjecture_on_iterated_circumcentres#comment Fri, 08 Jun 2007 02:52:17 +0200 mdevos 357 at http://openproblemgarden.org