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Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

For a plane curve, the tangential angle phi is defined by rhodphi=ds, (1) where s is the arc length and rho is the radius of curvature. The tangential angle is therefore ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...

A lossless data compression algorithm which uses a small number of bits to encode common characters. Huffman coding approximates the probability for each character as a power ...

The radius of a polygon's incircle or of a polyhedron's insphere, denoted r or sometimes rho (Johnson 1929). A polygon possessing an incircle is same to be inscriptable or ...

The tractrix arises in the following problem posed to Leibniz: What is the path of an object starting off with a vertical offset when it is dragged along by a string of ...

Let phi(z)=cz+c_0+c_1z^(-1)+c_2z^(-2)+... be an analytic function, regular and univalent for |z|>1, that maps |z|>1 conformally onto the region T preserving the point at ...

The parametric equations for a catenary are x = t (1) y = acosh(t/a), (2) giving the evolute as x = t-a/2sinh((2t)/a) (3) y = 2acosh(t/(2a)). (4) For t>0, the evolute has arc ...

A concho-spiral, also known as a conchospiral, is a space curve with parametric equations r = mu^ua (1) theta = u (2) z = mu^uc, (3) where mu, a, and c are fixed parameters. ...

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...