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The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

The Minkowski measure of a bounded, closed set is the same as its Lebesgue measure.

The statistical index P_M=(sump_nq_a)/(sump_0q_a), where p_n is the price per unit in period n and q_n is the quantity produced in period n.

A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

The Pappus configuration is the 9_3 configuration illustrated above that appears in Pappus's hexagon theorem. It is one of the three 9_3 configurations. The Levi graph of the ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...