A proof of Morley's miracle | #SoME3

Like last year, this video is in english because, it's my SoME3 project. I'll add french subtitles. I hope my accent isn't too awful. At the end of the video, the i = g_A^3g_B^3g_C^3 IS NOT the complex number i, it's just a name for an affine transformation that is shown to be the identity. Alain Connes image credit : "Alain Connes lors d'une conférence à l'IUT A à Villeneuve-d'Ascq (Nord, France)" by © Peter Potrowl (https://www.sitemai.eu/) Link to A. Connes' article : http://www.numdam.org/item/PMIHES_199... Link to A. Connes' article about symetries in 'Pour la science' (02/2001) : https://alainconnes.org/wp-content/up... animations made using Manim : https://www.manim.community/ All the python code of the video will be added to my github account, so check it out if you're interested. Here is the link to my github : https://github.com/MatheFysyk I hope you'll enjoy this video which took a little more than a month to make. If you have any suggestion or critic to help me and so that I can improve my work, don't hesitate to tell me. 00:00 Introduction 00:35 Morley's theorem 02:03 Classical equilateral triangle characterization in the complex plane 06:55 The dihedral group 08:25 The affine group over R 09:32 The affine group over C 12:05 Complex affine rotations 12:44 Proof setup 14:42 Trisector intersections as fixed points of affine rotations 15:40 A. Connes' proof 17:51 Does the theorem hold true in non-Euclidean geometries ? 18:40 Outroduction