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Analysis

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

A hedgehog is an envelope parameterized by its Gauss map (Martinez-Maure 1996). Viewed another way, a hedgehog is a Minkowski difference of a convex body (Martinez-Maure ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.