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The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

The mixtilinear triangle is the triangle connecting the centers of the mixtilinear incircles. It has trilinear vertex matrix (1) In has area (2) where Delta is the area of ...

A mental device used to aid memorization. Common mnemonics for mathematical constants such as e and pi consist of sentences in which the number of letters in each word give ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

A number b_(2n) having generating function sum_(n=0)^(infty)b_(2n)x^(2n) = 1/2ln((e^(x/2)-e^(-x/2))/(1/2x)) (1) = 1/2ln2+1/(48)x^2-1/(5760)x^4+1/(362880)x^6-.... (2) For n=1, ...

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

Given a elliptic modulus k in an elliptic integral, the modular angle alpha is defined by k=sinalpha. An elliptic integral is written I(phi|m) when the parameter m is used, ...

A lattice which satisfies the identity (x ^ y) v (x ^ z)=x ^ (y v (x ^ z)) is said to be modular.

The important property of Fourier transforms that F_x[cos(2pik_0x)f(x)](k) can be expressed in terms of F[f(x)]=F(k) as follows, ...