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If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

The r-Hofstadter triangle of a given triangle DeltaABC is perspective to DeltaABC, and the perspector is called the Hofstadter point. The triangle center function is ...

A system for specifying points using coordinates measured in some specified way. The simplest coordinate system consists of coordinate axes oriented perpendicularly to each ...

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

The azimuthal coordinate on the surface of a sphere (theta in spherical coordinates) or on a spheroid (in prolate or oblate spheroidal coordinates). Longitude is defined such ...

The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the z-axis is the axis about which the ...