Maple 3 is due on Thursday 23 Oct 2003

Unstapled assignments will not be accepted.
The first line of the worksheet should include your name.

Plots must be rotated to a "nice" position and "look good (smooth)".
Plots must include axes and titles. Titles must include your name.


To plot the surface <x(u, v), y(u, v), z(u, v)> a <= u <= b, c <= v <= d
with Maple use plot3d([x(u, v), y(u, v), z(u, v)], u=a..b, v=c..d)

1&2  Plot the following surfaces from u=0..2, v=0..4 (from Test 3 Fall 98)
Each plot is separate.
  1a. <cos v, sin v, u>
  1b. <(2+u)cos 2v, (2+u)sin 2v, v>
  2a. <u cos v, u sin v, u>
  2b. <sin u cos v, sin u sin v, cos u>
There are a total of 4 plots for problems one and two.

3. Find parameteric equations for torus with radii one and two.
This is surface generated when the circle in the xz-plane
given by (x-2)^2+z^2=1 is rotated about the z-axis. Plot your
parametric equations. (Problem 38 in HH 17.5) [Note that a tubeplot
is NOT acceptable, you must have and plot the parametric equations
of the torus.] I only want to see 1 plot for problem 3.

4. Add a `knot' (This knot is called a trefoil knot). Do a `tubeplot' of
the curve below for 0 <= theta <= 6*Pi (3 times around) of r = r(theta) =
 <(2+cos(2*theta/3))*cos(theta),(2+cos(2*theta/3))*sin(theta),sin(2*theta/3)>
and display it twice, once alone and once with a copy of your torus.
(The trefoil is called a Torus Knot and now you know why.) [tubepoint has
a default option `radius=1' which is too big. Use a smaller radius like
1/10 or 1/5.] I only want to see 2 plots for problem 4

5.  Plot a Klein bottle. The following should help. The handle and
bulb `fit together' to make one smooth surface.
c:=.6;a:=.2;
plot1 the handle:
Range u=Pi/2..5*Pi/2,v=Pi/4..5*Pi/4
A:=c*(cos(v)*sin(v) -0.5 + a*sin(u)*sin(v)/sqrt(sin(v)^2+cos(2*v)^2));
B:=a*c*cos(u);
C:=cos(v)+a*c*sin(u)*cos(2*v)/sqrt(sin(v)^2+cos(2*v)^2);
parametric equations of this part of the surface [A, B, C]

plot2 the bulb: v=5*Pi/4..9*Pi/4
Range u=Pi/2..5*Pi/2,v=5*Pi/4..9*Pi/4
r:=sin(v)*cos(v) - (a+1/2);
A:=c* sin(u) * r;
B:= -c * cos(u) * r;
C:=cos(v);
parametric equations of this part of the surface [A, B, C]

I only want to see 1 plot for problem 5.

There is a picture of a Klein Bottle at
http://www.math.fsu.edu/~bellenot/class/s03/cal3/klein.pdf