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For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...

An extension of the secant method of root finding to higher dimensions.

The system of ordinary differential equations u^' = A+u^2v-(B+1)u (1) v^' = Bu-u^2v (2) (Hairer et al. 1987, p. 112; Zwillinger 1997, p. 136). The so-called full Brusselator ...

A paradox arising in the use of comparative adjectives. Suppose you have exactly two brothers, both of whom are older than you are. Then the following apparently false ...

The Buchstab function omega(u) is defined by the delay differential equation {uomega(u)=1 for 1<=u<=2; (uomega(u))^'=omega(u-1) for u>2 (1) (Panario 1998). It approaches the ...

A quartic curve with implicit equation (a^2)/(x^2)-(b^2)/(y^2)=1 (1) or a^2y^2-b^2x^2=x^2y^2 (2) and a,b>0. In parametric form, x = +/-acost (3) y = bcott. (4) The curvature ...

Although the inner shaded region has the same area as the outer shaded annulus, it appears to be larger. Since the rings are equally spaced, A_(inner) = pi·3^2=9pi (1) ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...