This website lets you see the action of Möbius transformations or the action of \(\mathrm{PSp}(4, \mathbb{R})\) on circles, points, etc. on the Riemann sphere. The methods to compute these transformations are described in the corresponding sections and in detail in [Leb23]. The project is based on ideas developed in [BK21].
\(\mathcal{Möb}\) | \(\mathrm{PSp}(4, \mathbb{R})\)
This site was created by Samuel Leblanc, under the supervision of Jean-Philippe Burelle, as part of the course Experimental Mathematics Lab at Université de Sherbrooke. The code relating to this site can be found on GitHub. The visualisations were made using CindyJS.
[BK21] Jean-Philippe Burelle and Ryan Kirk. Piecewise circular curves and positivity.
arXiv:2108.08680, 2021.
[Leb23] Samuel Leblanc. Transformations de cercles orientés tangents sur la sphère de Riemann (PDF). 2023.