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The radical circle of the Neuberg circles has circle function l=(a^2b^4-b^4c^2+a^2c^4-b^2c^4)/(bc(a^2b^2+a^2c^2+b^2c^2)), (1) which does not correspond to any Kimberling ...

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

Orthogonal involution, also called absolute involution, is the involution on the line at infinity that maps orthogonal directions to each other.

In the plane, if a line intersects one side of a triangle and misses the three vertices, then it must intersect one of the other two sides. This is a special case of the ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

A correspondence between two line segment ranges that are sections of one pencil by two distinct lines.

Let t, u, and v be the lengths of the tangents to a circle C from the vertices of a triangle with sides of lengths a, b, and c. Then the condition that C is tangent to the ...

The distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

The Schmitt-Conway biprism is a convex polyhedron found to be only aperiodically space-filling by Conway in 1993.