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Subject: "trajectories on the torus"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #400
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danieladaniela
Member since Nov-9-10
 Nov-09-10, 08:55 PM (EST)
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"trajectories on the torus"
 
   First of all, let me thank Prof. Bogomolny for this marvelous and ever-growing site.
I hope may be some reader can help me find an applet I saw some time ago, with winded cycles on the torus. That is to say, a closed curve which turns n times around one cycle and m times around the other. It is possible to modify the values and get a feel, also it was possible to modify parameters such as the thickness of the string-curve. May be some reader can help me? Thank you so very much.
Daniela

Mathematics is the essence of
freedom


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alexb
Charter Member
2660 posts		 Nov-10-10, 10:18 AM (EST)
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1. "RE: trajectories on the torus"
In response to message #0
 
   Thank you for the kind words.

I never had an applet like that but I do remember seeing one. I'll post a link here if I find it.


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alexb
Charter Member
2660 posts		 Nov-10-10, 10:23 AM (EST)
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2. "RE: trajectories on the torus"
In response to message #1
 
   Here's one:

https://www.javaview.de/vgp/tutor/torusknot/PaTorusKnot.html


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danieladaniela
Member since Nov-9-10
 Nov-10-10, 01:33 PM (EST)
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3. "RE: trajectories on the torus"
In response to message #2
 
   Thank you so very much!

Mathematics is the essence of
freedom


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alexb
Charter Member
2660 posts		 Nov-13-10, 08:33 AM (EST)
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4. "RE: trajectories on the torus"
In response to message #3
 
   I believe I made a slight improvement to the original applet:

https://www.cut-the-knot.org/Curriculum/Geometry/PaTorusKnot.shtml


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Daniela
guest
 Nov-19-10, 08:52 AM (EST)
 
5. "RE: trajectories on the torus"
In response to message #4
 
   Thank you so very much!
Other readers interested in the subject or in teaching it (the torus is inexhaustible, every teacher has more to learn, pick up Arnold's books if you don't believe), may enjoy also the webpage "shredding a torus" on this site.
Also "The shape of space" and the free programs at geometrygames.org from Jeff Weeks and the Geometry Center resources.
This is a good place, i think, to suggest children to pass from the physical torus to the dynamical system torus and in general introduce "abstract" coordinates well before children calculate q and qdots:
https://www.learner.org/courses/mathilluminated/interactives/robots/

Have a great weekend and thanks again
Daniela


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