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In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

The so-called reaching algorithm can solve the shortest path problem (i.e., the problem of finding the graph geodesic between two given nodes) on an m-edge graph in O(m) ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

The Riemann-Siegel integral formula is the following representation of the xi-function xi(s) found in Riemann's Nachlass by Bessel-Hagen in 1926 (Siegel 1932; Edwards 2001, ...

The rule which determines the orientation of the cross product u×v. The right-hand rule states that the orientation of the vectors' cross product is determined by placing u ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

The second Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+2pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...

A fractal which can be written as a Lindenmayer system with initial string "YF", string rewriting rules "X" -> "YF+XF+Y", "Y" -> "XF-YF-X", and angle 60 degrees.

The silver constant is the algebraic number given by S = (x^3-5x^2+6x-1)_3 (1) = 2+2cos(2/7pi) (2) = 3.246979603... (3) (OEIS A116425), where (P(x))_n denotes a polynomial ...

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 ...