Search Results for ""

Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) (1) is the multinomial coefficient ...

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, ...

The inverse curve of the circle with parametric equations x = acost (1) y = asint (2) with respect to an inversion circle with center (x,y) and radius R is given by x_i = ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

The half-altitude circle is the circumcircle of the half-altitude triangle. The circle function is given by l=(f(a,b,c))/(128a^2b^3c^3cosAcosBcosC), (1) where (2) which is ...

The second Neuberg circle is the circumcircle of the second Neuberg triangle. The center has center function which is not a Kimberling center. Its radius is slightly ...

A circle surrounded by a square looks larger than the same circle surrounding a square.

The third Lemoine circle, a term coined here for the first time, is the circumcircle of the Lemoine triangle. It has center function alpha=(f(a,b,c))/a, (1) where f(a,b,c) is ...

The cut elimination theorem, also called the "Hauptsatz" (Gentzen 1969), states that every sequent calculus derivation can be transformed into another derivation with the ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...