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Consider an n-dimensional deterministic dynamical system x^_^.=f^_(x) and let S be an n-1-dimensional surface of section that is traverse to the flow, i.e., all trajectories ...

There are no tilings of the equilateral triangle of side length 7 by all the polyhexes of order n=4. There are nine distinct solutions of all the polyhexes of order n=4 which ...

All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

The Pythagorean means are the three "classic" means A (the arithmetic mean), G (the geometric mean), and H (the harmonic mean) are sometimes known as the Pythagorean means. ...

The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

Quantile-quantile plots (also called q-q plots) are used to determine if two data sets come from populations with a common distribution. In such a plot, points are formed ...

Given a straight segment of track of length l, add a small segment Deltal so that the track bows into a circular arc. Find the maximum displacement d of the bowed track. The ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

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 ...