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The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

A parallelotope whose edges are all mutually perpendicular. The orthotope is a generalization of the rectangle and cuboid.

Consider a reference triangle DeltaABC and any given point P. The perpendiculars to AP, BP and CP respectively meet BC, AC and AB in three collinear points defining line l. ...

The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

A curve y(x) is osculating to f(x) at x_0 if it is tangent at x_0 and has the same curvature there. Osculating curves therefore satisfy y^((k))(x_0)=f^((k))(x_0) for k=0, 1, ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

For an n-dimensional map, the Lyapunov characteristic exponents are given by sigma_i=lim_(N->infty)ln|lambda_i(N)| for i=1, ..., n, where lambda_i is the Lyapunov ...

If f(x) is a monotonically increasing integrable function on [a,b] with f(b)<=0, then if g is a real function integrable on [a,b], ...

Let A=a_(ij) be a matrix with positive coefficients and lambda_0 be the positive eigenvalue in the Frobenius theorem, then the n-1 eigenvalues lambda_j!=lambda_0 satisfy the ...