These knots are called torus knots because they can be realized on a torus.
No knot can be realized on a sphere.
All yellowish pictures are anaglyphs. They are computed with small eye separation
so that one can also view them, non-stereo, without red-green glasses.
This 19-2-torus knot can easily be imagined to lie on a torus.
Note that this and the previous knot are “alternating”, which means:
underpasses and overpasses alternate. An alternating knot cannot be
realized with fewer crossings if the knot is without an “isthmus”.
A crossing is called an 'isthmus', if a (diagonal) cutting through the
crossing decomposes the knot into two pieces.
This 7-3-knot is not alternating since the underpasses and overpasses
occur in pairs.
This animation shows how a 3-2-knot is deformed into a 2-3-knot. We use the
'conformal inside-out rotation' which is explained for the
Clifford Torus
.
These knots are computed as if the square rod were elastic and the color bands
were straight before the rods were bent into these knots.
This 3-2-knot is shown with 'osculating circles', these circles have the same
curvature as the space curve has at the points of contact.
A knot which looks rather simple in its most symmetric form may look much more
complicated when viewed from a different direction.
