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The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The second-order ordinary differential equation y^('')+(y^')/x+(1-(nu^2)/(x^2))y=(x-nu)/(pix^2)sin(pinu) whose solutions are Anger functions.

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian ...

A series of the form sum_(n=0)^inftya_nJ_(nu+n)(z), (1) where nu is a real and J_(nu+n)(z) is a Bessel function of the first kind. Special cases are ...

The bifoliate is the quartic curve given by the Cartesian equation x^4+y^4=2axy^2 (1) and the polar equation r=(8costhetasin^2theta)/(3+cos(4theta))a (2) for theta in [0,pi]. ...