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Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

Half a zip-pair.

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

Half of a sphere cut by a plane passing through its center. A hemisphere of radius r can be given by the usual spherical coordinates x = rcosthetasinphi (1) y = ...

Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

The dimension of a special series can never exceed half its order.

A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a ...