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Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The Patterson graph is the graph whose vertices are the 22880 centers of the Sylow 3-groups of the Suzuki group and in which two vertices are adjacent whenever they generate ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

A class of map projections in which the parallels are represented by a system of non-concentric circular arcs with centers lying on the straight line representing the central ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...