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The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

A cubic equation is an equation involving a cubic polynomial, i.e., one of the form a_3x^3+a_2x^2+a_1x+a_0=0. Since a_3!=0 (or else the polynomial would be quadratic and not ...

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x)=a_3x^3+a_2x^2+a_1x+a_0. An equation involving a cubic polynomial is called a ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

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 ...

A quantity is said to be exact if it has a precise and well-defined value. J. W. Tukey remarked in 1962, "Far better an approximate answer to the right question, which is ...