Uses maple 18 software to demonstrate the kinds of math animations that can be used for inclusion on your webpages. You can use these codes to create your own designs and edit them to your liking. Three examples which show that math can be fun, as well as, instructional; although this program is an analytical software intended for engineers.

1. Commit to an animation

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 comes bundled with paintshop pro(a rather old program). You should be able to go someplace like lunapic to edit the gif as well.

Popular Designs (Modified codes from Maple 8ish)

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 build the case for 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. This was an example of maple's 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

John Carroll University Mathematics Department

The math 696 logo

Jeffrey F. Brock Research This was really helpful since I lost some of my start up models.

Powered by WebRing.

1. Commit to an animation

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 comes bundled with paintshop pro(a rather old program). You should be able to go someplace like lunapic to edit the gif as well.

Popular Designs (Modified codes from Maple 8ish)

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 build the case for 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. This was an example of maple's 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);

The math 696 logo

Jeffrey F. Brock Research This was really helpful since I lost some of my start up models.