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A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are equipotential curve, isarithm, and isopleth. A plot of several ...

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

The path of an object through phase space.

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...

Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

While the above figure appears to be a sequence of nested squares, it actually consists of a single square spiral.

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

"Fluxion" is the term for derivative in Newton's calculus, generally denoted with a raised dot, e.g., f^.. The "d-ism" of Leibniz's df/dt eventually won the notation battle ...

Wallis's constant is the real solution (x^3-2x-5)_1=2.0945514815... (OEIS A007493) to the cubic equation x^3-2x-5=0. It was solved by Wallis to illustrate Newton's method for ...