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Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

Fok (1946) and Hazewinkel (1988, p. 65) call v(z) = 1/2sqrt(pi)Ai(z) (1) w_1(z) = 2e^(ipi/6)v(omegaz) (2) w_2(z) = 2e^(-ipi/6)v(omega^(-1)z), (3) where Ai(z) is an Airy ...

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

The Heesch number of a closed plane figure is the maximum number of times that figure can be completely surrounded by copies of itself. The determination of the maximum ...

A number n such that sigma^2(n)=sigma(sigma(n))=2n, where sigma(n) is the divisor function is called a superperfect number. Even superperfect numbers are just 2^(p-1), where ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

Let theta(t) be the Riemann-Siegel function. The unique value g_n such that theta(g_n)=pin (1) where n=0, 1, ... is then known as a Gram point (Edwards 2001, pp. 125-126). An ...