This worksheet has an error when executing EulerLagrange.

How can this error be avoided?

Spring_Pendulum.mw

Initial text in the uploaded worksheet describes an attempt to partially tile the Poincare disk and asks to be shown how a known complex transformation can be used to accomplish this.

 Poincare_tiling.mw

The worksheet below contains the desired hyperbolic action and asks for the specific transformation that performs it.

Hyperbolic_Transformation.mw

I have corrected the above worksheet so that the Poincare disk is now centred at [0,0].

I hope this helps you answer my question

In the worksheet below is an equation for non-Euclidean lines. How can Maple plot these?

NonEuclideanLines.mw

This worksheet creates geodesics in the Poincare disk by transformation of a series of circles of diminishing radii in the complex plane.

The intersections of the geodesics are meant to create the first few pentagonal uniform tilings in the Poincare disk.

I do not know the mathematically correct way to create such a display, so the radii of the circles are only a trial and error approximation.

What Maple code will provide the radii of the complex circles which produce an accurate uniform pentagonal tiling?

Is there a better overall strategy for producing uniform tilings of the Poincare disk? 

HyperbolicTiling.mw