By Catherine Cavagnaro, William T. Haight II

Containing greater than 1,000 entries, the Dictionary of Classical and Theoretical arithmetic specializes in mathematical phrases and definitions of serious value to training mathematicians and scientists. This single-source reference presents operating definitions, meanings of phrases, similar references, and an inventory of other phrases and definitions. The dictionary is certainly one of 5 constituent works that make up the casebound CRC complete Dictionary of arithmetic.

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The game GX is determined if one of the two players has a winning strategy. developable surface A ruled surface is a surface swept out by a straight line (called the generator) moving through space. It can be given a parameterization of the form X(u, v) = C(u) + vD(u) where C is a curve and C (u)×D(u) does not vanish. If the tangent plane to the surface at any point is tangent along the entire generator through the point, then the surface is called a developable surface. For example, a cylinder is a developable surface, as is a cone.

N) < 2n. For example, 16 is deficient, since 1 + 2 + 4 + 8 + 16 = 31 < 32 . Compare with abundant number, perfect number. definition by recursion See recursion. , the class of all sets B of natural numbers which are Turing equivalent to A. A degree of unsolvability is often called a Turing degree, or simply a degree. As an example, if A is a recursive (computable) set, then deg(A) consists of all recursive (computable) sets. However, if A is computably (recursively) enumerable, then deg(A) does not consist of all computably enumerable sets.

Other coproducts of X and Y can be formed by choosing different sets Y . corresponding angles Let two straight lines lying in R2 be cut by a transversal, so that angles x and y are a pair of alternating interior angles, and y and z are a pair of vertical angles. Then x and z are corresponding angles. cotangent bundle Let M be an n-dimensional differentiable manifold of class C r . Consider T (M), the union over p ∈ M of all the vector spaces Tp (M) of vectors tangent to M at p. Define π : T (M) → M by π(Tp (M)) = p.