By Catherine Cavagnaro, II, William T. Haight

Containing greater than 1,000 entries, the Dictionary of Classical and Theoretical arithmetic specializes in mathematical phrases and definitions of severe significance to practising mathematicians and scientists. This single-source reference offers operating definitions, meanings of phrases, comparable references, and a listing of other phrases and definitions. The dictionary is considered one of 5 constituent works that make up the casebound CRC complete Dictionary of Mathematics.

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Concentric spheres center. Spheres with the same cone A solid in R3 , bounded by a region in a plane (the base) and the surface formed by straight lines (the generators) which join points of the boundary of the base to a fixed point (the vertex) not in the plane of the base. , at another point is sometimes also called a cone. A cone may be viewed as a quadratic surface, whose equation is Ax 2 + By 2 + Cz2 = 0 (A, B, C = 0). When A = B, it is a right circular cone (also called a cone of revolution); if A=B, it is an oblique circular cone.

The conical surface consists of two concave pieces positioned symmetrically about the vertex. It is quadric if the directrix is a conic. A circular conical surface is one whose directrix is a circle and whose vertex is on the line perpendicular to the plane of the circle and passing through the center of the circle. , (A11 ∨ · · · ∨ A1m1 ) ∧ · · · ∧ (An1 ∨ · · · ∨ Anmn ), where each Aij , 1 ≤ i ≤ n, 1 ≤ j ≤ mi , is either a sentence symbol or the negation of a sentence symbol. Every well-formed propositional formula is logically equivalent to one in conjunctive normal form.

If the expression consists of only a finite number of fractions, the expression is called a finite continued fraction and is (obviously) a rational number. See also finite continued fraction. An infinite simple continued fraction is one of the form a0 + 1 a1 + 1 a2 + 1 a3 + 1 .. where each of the ai is an integer. See also convergence of a continued fraction. continuous function A function f from a topological space X to a topological space Y such that, for each open U ⊆ Y , the set f −1 (U ) is open in X.