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The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

A linear functional on a smooth differential form.

The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius b<a, where a is the radius of a rolling circle. Curtate ...

The evolute of the curtate cycloid x = at-bsint (1) y = a-bcost (2) (with b<a) is given by x = (a[-2bt+2atcost-2asint+bsin(2t)])/(2(acost-b)) (3) y = ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

The point on the positive ray of the normal vector at a distance rho(s), where rho is the radius of curvature. It is given by z = x+rhoN (1) = x+rho^2(dT)/(ds), (2) where N ...

K=(dT)/(ds), where T is the tangent vector defined by T=((dx)/(ds))/(|(dx)/(ds)|).

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...