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The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...

Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

The Mandart circle is the circumcircle of the extouch triangle. It has center at Kimberling center X_(1158), which has trilinear center function (1) and radius ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

Let T_1 be the point at which the J_1-excircle meets the side A_2A_3 of a triangle DeltaA_1A_2A_3, and define T_2 and T_3 similarly. Then the lines A_1T_1, A_2T_2, and A_3T_3 ...