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As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

The latitude of a point on a sphere is the elevation of the point from the plane of the equator. The latitude delta is related to the colatitude (the polar angle in spherical ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

Minesweeper is single-player logic-based computer game played on rectangular board whose object is to locate a predetermined number of randomly-placed "mines" in the shortest ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

A surface possessing a saddle point.

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...