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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 ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

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 ...

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

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 ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...