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Lehmer (1938) showed that every positive irrational number x has a unique infinite continued cotangent representation of the form x=cot[sum_(k=0)^infty(-1)^kcot^(-1)b_k], (1) ...

On a Riemannian manifold M, there is a canonical connection called the Levi-Civita connection (pronounced lē-vē shi-vit-e), sometimes also known as the Riemannian connection ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

The pseudosquare L_p modulo the odd prime p is the least nonsquare positive integer that is congruent to 1 (mod 8) and for which the Legendre symbol (L_p/q)=1 for all odd ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...