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Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

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 ...

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

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, ...

The exsecant is a little-used trigonometric function defined by excsc(x)=cscx-1, where cscx is the cosecant.

A class of processes which attempt to round off a domain and simplify its theory by adjoining elements.

A function whose value increases more quickly than any polynomial is said to be an exponentially increasing function. The prototypical example is the function e^x, plotted ...

The Cartesian product of a finite or infinite set of modules over a ring with only finitely many nonzero entries in each sequence.