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A ring of fractions that coincides with the localization with respect to the set of all non-zero divisors.

The radial curve of the tractrix x = a(t-tanht) (1) y = asecht (2) with radiant point (x_0,y_0) is the kappa curve x_r = x_0+atanht (3) y_r = y_0+asinhttanht. (4)

To translate an object means to perform a translation. A translate of a mathematical object means a shifted (i.e., translated) version of the object. Hence, one can speak of ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...

The Tristan Edwards projection is a cylindrical equal-area projection which uses a standard parallel of phi_s=37.383 degrees.

Two quantities a and b which are not equal are said to be unequal, and this relationship can be denoted a!=b.

A random number which lies within a specified range (which can, without loss of generality, be taken as [0, 1]), with a uniform distribution.

The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

An operator U satisfying U^|U = 1 (1) UU^| = 1, (2) where U^| is the adjoint.

The depth of a vertex v in a rooted tree as the number of edges from v to the root vertex. A function to return the depth of a vertex v in a tree g may be implemented in a ...