Playing with a Torus
ACTIVITIES
1) Move the sliders "BigRadius" and "SmallRadius" and observe their effect on the torus.
2) Look at the parameterisation of the torus (surface S) and justify what you observed in the previous activity.
3) Observe the coordinate curves displayed on the texture of the surface. Check that they correspond to the meridians and parallels of the torus. Move the sliders "longitude" and "latitude" to convince yourself that each point in the torus is the crossing point of a unique meridian and a unique parallel. The corresponding longitude and latitude are called the "toric coordinates" of the point.
4) Locate the point of toric coordinates (Pi/2, Pi/3). What are the toric coordinates of the opposites points? (There is more than one sense of "opposite point" on the torus!)
5) Make visible the curve "knot", by clicking on its bullet. Move the slider "p" until you understand its effect on the curve.
6) Set "p" back to the value 1. Now, move the slider "q" until you understand its effect on the curve.
7) Move both sliders "p" and "q" and describe the behaviour on the curve.
8) Look at the definition of the curve. What role do "p" and "q" play on it? Relate this to the behaviour described on the previous activity.