These Jupyter notebooks are for discussion and discovery of Lie-Möbius sphere geometry through the usage of the dedicated MoebInv package [4] .
To jump to execution of a notebook click its ⚙CoLab button at the end of description. All these notebooks are included in
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Installing the libraries and integration with GUI: To install the libraries on CoLab or your Ubuntu-18.04 desktop you need to execute only one cell. Python/Jupyter code is bidirectionally integrated with Graphical User Interface (GUI). ⚙CoLab, or 👁 HTML view
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Euclidean and Lobachevsky lines: This notebook provides a minimal example and shows how to make initial software installation. ⚙CoLab or 👁 HTML view
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Nine point theorem: Some non-trivial illustrations and extensions of this celebrated statement. ⚙CoLab or 👁 HTML View
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Example of symbolic computations: An analytic proof of a simple geometric statement. ⚙CoLab or 👁 HTML view
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Example of automatically generated Python script: it was produced from the GUI and post-processed by p2j (Python to Jupyter) utility. ⚙CoLab or 👁 HTML view
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What is a cycle, anyway? A pedestrian introduction of the key concept of Lie-Möbius sphere geometry. ⚙CoLab or 👁 HTML view
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What is PyGiNaC, anyway? An overview of main features of pyGiNaC---the backbone of these notebooks. ⚙CoLab or 👁 HTML view
The complete set of computer-assisted exercises from the book [2] presented as Jupyter notebooks. See complete list on the separate pages:
⚙GitHub or 👁 HTML view.
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Kleinian group A group of fraction-linear transformations generated by several reflections in cycles. ⚙CoLab or 👁 HTML view
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Recursive reflections Filling circular gaps by recursive inversion inside of them. ⚙CoLab or 👁 HTML view
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Modular group action Action of the modular group SL(2,Z) generated by shifts and an inversion. ⚙CoLab or 👁 HTML view
- Vladimir V. Kisil, MoebInv: Symbolic, numeric and graphic manipulations in non-Eclidean geometry, SourceForge repository, 2004-2019.
2. Vladimir V. Kisil. Geometry of Möbius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL(2,R). Imperial College Press, London, 2012. Includes a live DVD.
- Vladimir V. Kisil, MoebInv notebooks, 2019.
4. Vladimir V. Kisil, MoebInv: C++ Libraries for Manipulations in Non-Euclidean Geometry, SoftwareX, 11(2020), 100385. arXiv:1912.03489.