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A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...

The bifolium is a folium with b=0. The bifolium is a quartic curve and is given by the implicit equation is (x^2+y^2)^2=4axy^2 (1) and the polar equation ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...