@acer 

Thanks for the help. Using the code of the Mathapp is exactly the goal of my approach (for not to reinvent the wheel;)) Is there a way to generalize the process for a series of existing Math app in the software?

@tomleslie  Thanks !

@tomleslie  Thanks.Is there a way to display Fibonacci numbers too?

@acer Thanks

@Carl Love  Thanks for your idea.. My goal is to export the animation to GIF format ( for  sharing..).

The Explore command don t keep animation dimension

Thanks

@Carl Love  When i add animate command, i receive Error Message

@Carl Love 

This is my idea..

 ROTATIONConiquesEllipseAnimation.mw

@Carl Love  Thanks.

I think that more simple with parametric equation..

ROTATIONConiquesEllipseAnimation.mw

i tried this sequence to obtain animation of my Ellipse

Thanks for ideas 

EllipseMaple.mw

@vv Perfect ! 

@vv  How to do this with plot3d and animate?

@Kitonum  great ! Thanks

@Kitonum  its exactly what i need ! Thanks

i try this solution but is not optimal

AnimationShadebetween.mw

@acer  Thanks !