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The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...

Rational numbers are countable, so an order can be placed on them just like the natural numbers. Although such an ordering is not obvious (nor unique), one such ordering can ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

The salinon is the figure illustrated above formed from four connected semicircles. The word salinon is Greek for "salt cellar," which the figure resembles. If the radius of ...

The fractal J(-3/4,0), where J is the Julia set. It slightly resembles the Mandelbrot set.

By analogy with the sinc function, define the sinhc function by sinhc(z)={(sinhz)/z for z!=0; 1 for z=0. (1) Since sinhx/x is not a cardinal function, the "analogy" with the ...

A sinusoidal spiral is a curve of the form r^n=a^ncos(ntheta), (1) with n rational, which is not a true spiral. Sinusoidal spirals were first studied by Maclaurin. Special ...

The compound of the snub cube and its dual, the pentagonal icositetrahedron. Surprisingly, the tribonacci constant t is intimately related to the metric properties of the ...