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P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

A knot property, also called the twist number, defined as the sum of crossings p of a link L, w(L)=sum_(p in C(L))epsilon(p), (1) where epsilon(p) defined to be +/-1 if the ...

The Dottie number is the name given by Kaplan (2007) to the unique real root of cosx=x (namely, the unique real fixed point of the cosine function), which is 0.739085... ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.

The nth coefficient in the power series of a univalent function should be no greater than n. In other words, if f(z)=a_0+a_1z+a_2z^2+...+a_nz^n+... is a conformal mapping of ...