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Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...

A two-person game where each of the players can take as long as he likes to prepare his move, but the other can take advantage of his hesitation. In this conflict situation, ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

A surface of revolution which is generalization of the ring torus. It is produced by rotating an ellipse having horizontal semi-axis a, vertical semi-axis b, embedded in the ...

The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

The Euler triangle formula states that the distance d between the incenter and circumcenter of a triangle is given by d^2=R(R-2r), where R is the circumradius and r is the ...

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the ...