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X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

In the above figure, the identical squares A, B, C appear different in width and height, because subdividing a space makes it appear larger. A different orientation can also ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

(1) for p in [-1/2,1/2], where delta is the central difference and S_(2n+1) = 1/2(p+n; 2n+1) (2) S_(2n+2) = p/(2n+2)(p+n; 2n+1), (3) with (n; k) a binomial coefficient.

A curve investigated by Talbot which is the ellipse negative pedal curve with respect to the ellipse's center for ellipses with eccentricity e^2>1/2 (Lockwood 1967, p. 157). ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...