Knots on a Torus
The applet below displays the curves that wind on the surface of a torus a prescribed number of times. The applet makes use of the JavaView library and is a slight modification (hopefully, an improvement) of one of their tutorial samples.
Torus is a two dimensional surface defined in a 3d space, which means that, to describe a torus, one needs three coordinates, say
x(u, v) = (R + r cos v) cos u,
y(u, v) = (R + r cos v) sin u,
z(u, v) = r sin v.
Torus is described by a circle of radius r centered at the points of circle
The curves that the applet displays are defined with a single parameter,
u(t) = Ut, v(t) = Zt, t ∈[0, 2π].
Parameter U tells us how many times the curve winds around z-axis. Parameter Z gives the number of turns around the basic circle,
|What if applet does not run?|
Copyright © 1996-2018 Alexander Bogomolny