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The Lehmer cotangent expansion for which the convergence is slowest occurs when the inequality in the recurrence equation b_k>=b_(k-1)^2+b_(k-1)+1. (1) for ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

The low-level language of topology, which is not really considered a separate "branch" of topology. Point-set topology, also called set-theoretic topology or general ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

A projection of the Veronese surface into three dimensions (which must contain singularities) is called a Steiner surface. A classification of Steiner surfaces allowing ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...