# 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 & AnimationsMathematical Animations for Your Web Pages