This worksheet animates the motion of an object (say, a cube which slides frictionlessly) on a rotating carousel. The cube is not self-propelled.

How can the worksheet be modified to handle the combination of the carousel motivated motion and the cube's own generated motion, caused by, say, by a few strategically placed thrusters?

The cube's own generated path could be a straight line, or a curve such as an ellipse. The cube's own motion could have a constant velocity or be accelerating.

Carousel_dynamics.mw

Is there a command which will analyze a procedure and list all unreferenced global and local sequence entries?

The uploaded worksheet begins to uniformly tile the Poincare disk with pentagons using hyperbolic reflection .

Although relatively easy to create the central pentagon and the first adjacent pentagon, it becomes increasingly difficult to determine which lines to reflect to create the remaining pentagons in the first tier adjacent to the central pentagon and more so to create the pentagons of the second tier adjacent to those in the first tier and so on.

Is there a better technique for accomplishing this?

In particular can Mobius tranformations be employed to do this? If so, please replay with or point to a working example of this for me to follow.

 Tile_Poincare_disk.mw

Sorry, I forgot that respondents to this question must establich their own link to the DirectSearch package.

The worksheet below includes a sample use of the Mobius transformation which produces a hyperbolic reflection of a point in the Poincare disk, followed by my attempt to produce the same result from first principles in a procedure.

Do I misunderstand the Mobius transformation and its use and/or is my procedure incorrect? 

InversePoint.mw

Is there a way to directly code a complex conjugate such as z with overbar without using the verbose conjugate(z)?