Building a Surface from One Knot
In the previous section we used two torus knots to form the boundary
of a surface. In this section we will examine what surfaces result
from using a single curve as the boundary of a surface.
Question #6
Consider a torus knot of type (2,1). You parametrized and
sketched this knot in Question #1.
- Parametrize the surface generated by
inserting a line segment from the point
T(2s,s) to the point T(2s,s+Pi).
Hint: Let s=0 to get your bearings.
Notice that you are connecting a line segment between two different
points on the same curve.
- What surface is this? What is its boundary?
- Include a plot of this surface in your lab writeup with
the outside portion of the surface colored red and the
inside portion of the surface colored green.
Question #7
- Repeat the previous problem for the torus knot of
type (2,3)
- Conjecture what surface is formed by connecting the points
T(2s,ns) to T(2s,ns+Pi) when n
is an odd integer.
Up: Introduction
Previous: Building a Surface from Torus Knots
Frederick J. Wicklin<fjw@geom.umn.edu>
Document Created: Thu Feb 23 1995
Last modified: Sat Feb 25 16:00:36 1995