Math Animations

Maple 18


Using Maplesoft 18 software to demonstrate the kinds of math animations that you can make for inclusion on your webpages.

1. Commit to a math animation in Maplesoft.
2. Edit the size.
3. Experiment with the colors and rotating the image.
4. Export the image as a gif.
5. You might have to use an additional editor for animation to reduce the speed of the animation, crop out extra white space, add transparency or loop it. A popular one named "Animation Shop" comes bundled with Paintshop Pro. You should be able to go someplace like Luna Pic to edit the gif as well.

Favorites

(These codes come straight from the Maple 8 book)

1. Parametrized 3D surface. Shows how the surface (3 dependent variables) can be determined by the 2 parameters.
with(plots) animate3d((1-2*abs(1-t))*x*exp(-x^2-y^2), x = -3 .. 3, y = -3 .. 3, t = 0 .. 2, frames = 20);


2. Solid of Revolution. Using the space curve (drawn in y-z) to create the cylinder plot.
with(plots): with(plottools): f := t -> t^3/2-2*t^2+2*t+1: start := spacecurve([0,t,f(t)],t=0..3,thickness=3): pic := n-> cylinderplot(f(z),theta=0..n*2*Pi/30,z=0..3): display(start,seq(rotate(pic(n),Pi/2,Pi/2,0),n=1..30), insequence=true,axes=normal,tickmarks=[0,0,0]);


3. Trefoil Knot. You can create a warped cylinder along a 3D curve, which is the tubeplot function.
with(plots) with(plots): TieKnot := proc(n :: posint) local i, t, curve, picts; curve := [-6*cos(t) - 2*cos(5*t) + 15*sin(4*t), -15*cos(2*t) + 7*sin(t) -2*sin(5*t), 10*cos(6*t)]: picts := [seq(tubeplot(curve,t=0..2*Pi*i/n, radius=3), i=1..n)]; display(picts, insequence=true); end; TieKnot(48);

Additional References

Maplesoft Graphics & Animations
Mathematical Animations for Your Web Pages