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The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...

Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

The fish curve is a term coined in this work for the ellipse negative pedal curve with pedal point at the focus for the special case of the eccentricity e^2=1/2. For an ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...