Introduction
Here are some links to a table of knots, up to 9 crossings, built as three-dimensional objects.
If you can achieve stereoscopic vision with two adjacent pictures, you can see the knots "in 3D".
Options:
- applets with larger width in pixels (for those who can achieve stereoscopic vision easily and/or use high resolution screen or small monitors).
- applets with smaller width in pixels (for those who have difficultty in achieving stereoscopic vision and/or use low screen resolutions or large monitors).
Mathematica
was used to construct each curve; each figure in the table was made with OpenGLViewer
and points to Java applet, which uses LiveGraphics3D.
(If you have never used this program before, see the corresponding help
on how to manipulate the object with the mouse).
Translated for Atractor by Gabriela Chaves, from its original version in Portuguese. Atractor is grateful for her cooperation.
(*) The routines for the creation of the 3D curves were written essentially by Vítor Sousa, according to a detailed plan previously suggested in the scope of "Estágio". (Ramo Educacional da Licenciatura em Matemática - F.C.U.P - 2000/2001.). That subject acted as a guideline for a first contact with Mathematica.
Difficulty level: University