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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 ...

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

A Brunnian link is a set of n linked loops such that each proper sublink is trivial, so that the removal of any component leaves a set of trivial unlinked unknots. The ...

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 ...

A highly structured geometric object used to study groups which act upon them.

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 ...

The integral transform defined by (Kphi)(x)=int_0^infty(x^2-t^2)_+^(lambda/2)P_nu^lambda(t/x)phi(t)dt, where y_+^alpha is the truncated power function and P_nu^lambda(x) is ...