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Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

Given an original triangle (thick line), find the medial triangle (outer thin line) and its incircle. Take the pedal triangle (inner thin line) of the medial triangle with ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

Polynomials P_k(x) which form the Sheffer sequence for g(t) = (2t)/(e^t-1) (1) f(t) = (e^t-1)/(e^t+1) (2) and have generating function ...

A primitive Pythagorean triple is a Pythagorean triple (a,b,c) such that GCD(a,b,c)=1, where GCD is the greatest common divisor. A right triangle whose side lengths give a ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...