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Given a function of two variables df = (partialf)/(partialx)dx+(partialf)/(partialy)dy (1) = udx+vdy, (2) change the differentials from dx and dy to du and dy with the ...

The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters x:y:z=(2(b^2+c^2)-a^2)/(bc):(2(a^2+c^2)-b^2)/(ac): (2(a^2+b^2)-c^2)/(ab). (1) The ...

Let t(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Then if S_m=sum_(t(m))1/t, (1) then {S_m=0 (mod m^2) ...

Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known ...