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Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

The cochleoid, whose name means "snail-form" in Latin, was first considered by John Perks as referenced in Wallis et al. (1699). The cochleoid has also been called the oui-ja ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...