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Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

A phase curve is a plot of the solution to a set of equations of motion in a phase plane (or more generally, a phase space) as a function of time (Tabor 1989, p. 14). Phase ...

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

A phase portrait is a plot of multiple phase curves corresponding to different initial conditions in the same phase plane (Tabor 1989, p. 14). Phase portraits for simple ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...

Exponential growth is the increase in a quantity N according to the law N(t)=N_0e^(lambdat) (1) for a parameter t and constant lambda (the analog of the decay constant), ...

A continuous-time stochastic process W(t) for t>=0 with W(0)=0 and such that the increment W(t)-W(s) is Gaussian with mean 0 and variance t-s for any 0<=s<t, and increments ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...