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The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

A disjunction that is true if only one, but not both, of its arguments are true, and is false if neither or both are true, which is equivalent to the XOR connective. By ...

If there exists an A, this is written exists A. Similarly, "A does not exist" is written notexists A. exists is one of the two mathematical objects known as quantifiers. The ...

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

Consider a function f(x) in one dimension. If f(x) has a relative extremum at x_0, then either f^'(x_0)=0 or f is not differentiable at x_0. Either the first or second ...

Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

Values one step outside the hinges are called inner fences, and values two steps outside the hinges are called outer fences. Tukey calls values outside the outer fences far ...