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A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

Twin primes are pairs of primes of the form (p, p+2). The term "twin prime" was coined by Paul Stäckel (1862-1919; Tietze 1965, p. 19). The first few twin primes are n+/-1 ...

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...

Let lim stand for the limit lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...