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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 rectification is sometimes used to refer to the determination of the length of a curve. Rectification also refers to the operation which converts the midpoints of ...

A conical surface modeled after the shape of a seashell. One parameterization (left figure) is given by x = 2[1-e^(u/(6pi))]cosucos^2(1/2v) (1) y = ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

The equation of the curve of intersection of a torus with a plane perpendicular to both the midplane of the torus and to the plane x=0. (The general intersection of a torus ...

The "temperature" of a curve Gamma is defined as T=1/(ln((2l)/(2l-h))), where l is the length of Gamma and h is the length of the perimeter of the convex hull. The ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

A tube of radius r of a set gamma is the set of points at a distance r from gamma. In particular, if gamma(t) is a regular space curve whose curvature does not vanish, then ...