Torus Knot

From Math Images

Jump to: navigation, search
Image:inprogress.png
Torus Knot
In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3.

Basic Description

In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3.

A More Mathematical Explanation

Note: understanding of this explanation requires: *Differential Geometry

These knots lie on the following torus of revolution (having ellipses as meridian curves):

UNIQ [...]

These knots lie on the following torus of revolution (having ellipses as meridian curves):

x(t) = (aa + bb cos(u)) cos(v)
y(t) = (aa + bb cos(u)) sin(v)
z(t) = cc sin(u)

The knots are obtained by putting u = dd t, v = ee t. The parameters dd and ee should be integers, and the result is referred to as a (dd,ee) knot (The program used to make the image rounds dd and ee before using them.)




Teaching Materials

There are currently no teaching materials for this page. Add teaching materials.









If you are able, please consider adding to or editing this page!

Have questions about the image or the explanations on this page?
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.






Personal tools