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The conical spiral with angular frequency a on a cone of height h and radius r is a space curve given by the parametric equations x = (h-z)/hrcos(az) (1) y = (h-z)/hrsin(az) ...

A proposition which is consistent with known data, but has neither been verified nor shown to be false. It is synonymous with hypothesis.

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

A subgroup H of an original group G has elements h_i. Let x be a fixed element of the original group G which is not a member of H. Then the transformation xh_ix^(-1), (i=1, ...

Connectivity properties obey the following hierarchy: convex => star convex => pathwise-connected => connected.

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

A theorem in set theory stating that, for all sets A and B, the following equivalences hold, A subset B<=>A intersection B=A<=>A union B=B.

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

A polynomial P(x) that, when evaluated over each x in the domain of definition, results in the same value. The simplest example is P(x)=c for x in R and c a constant.