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The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

The difference H_2-H_1, where H_1 and H_2 are hinges. It is the same as the interquartile range for N=5, 9, 13, ... points.

For n>=3, there exist no additive finite and invariant measures for the group of displacements in R^n.

A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not ...

The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is A=1/2nR^2sin((2pi)/n)=3.

Let a spherical triangle have sides of length a, b, and c, and semiperimeter s. Then the spherical excess E is given by

The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

The radial curve of the logarithmic spiral is another logarithmic spiral.

A median triangle is a triangle whose sides are equal and parallel to the medians of a given triangle. The median triangle of the median triangle is similar to the given ...