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Johnson's theorem states that if three equal circles mutually intersect one another in a single point, then the circle passing through their other three pairwise points of ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

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 ...

The quotient space X/∼ of a topological space X and an equivalence relation ∼ on X is the set of equivalence classes of points in X (under the equivalence relation ∼) ...

An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

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 ...

The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) ...

The pedal curve of an ellipse with parametric equations x = acost (1) y = bsint (2) and pedal point (x_0,y_0) is given by f = ...

The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles (Kimberling 1998, p. 158). (The fact that the ...