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Let H_nu^((iota))(x) be a Hankel function of the first or second kind, let x,nu>0, and define w=sqrt((x/nu)^2-1). Then ...

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

Take x itself to be a bracketing, then recursively define a bracketing as a sequence B=(B_1,...,B_k) where k>=2 and each B_i is a bracketing. A bracketing can be represented ...

A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form x(u,v)=b(u)+vdelta(u), (1) where b is called the ...

The Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

Let I_A, I_B, and I_C be the vertices of the inner Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...