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A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

A diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns ...

The hyperbolic cotangent is defined as cothz=(e^z+e^(-z))/(e^z-e^(-z))=(e^(2z)+1)/(e^(2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik 2000, p. ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...