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Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

A curve which intersects some straight line in an infinity of points (but for which not every point lies on this curve).

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

The common axis of the three altitude planes of a trihedron.

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...