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A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

A closed two-form omega on a complex manifold M which is also the negative imaginary part of a Hermitian metric h=g-iomega is called a Kähler form. In this case, M is called ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...