A Theorem concerning Six Points
نویسنده
چکیده
1. Introduction and statement of results. "Let three points be specified on a line. Then one of the points is in the interior of the line segment joining the other two, and one of the points is exterior to the line segment joining the other two." This elementary statement concerning the ordering of three points on a line is capable of various extensions. Thus, e.g., it is easy to prove the following: Let « + 2 points which are not all on an «-sphere be specified in E " , with some « + 1 of them linearly independent. Then one of the points must be in the interior of the «-sphere passing through the other « + 1 points, and one of the points must be exterior to the «-sphere passing through
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