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MaplePrimes Activity

These are questions asked by Earl

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.


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? 


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

This worksheet contains an unnamed theorem on page 202 of David Wells's book The Penguin Dictionary of Curious and Interesting Geometry.

Somehow I have uploaded both its contents and (a) link(s) to it.

What Maple code can animate and display, in turn, each of the portrayed pursuit paths?



Consider a target point T which moves at constant speed along a straight line, and a moving point P which at all times moves directly towards T. If P starts anywhere on the outermost ellipse, and T starts from a focus of the outer ellipse, then P always captures T at the same point, the centre of the ellipse.




The concentric ellipses, whose shape depends on the relative velocities of T and P, are isochrones, and the curves of pursuit are their isoclinal trajectories


Download Pursuit_problem

1) the two cylinders are centered on the x and z axis respectively

2) any two intersecting cylinders

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