Hexagrammum Mysticum 10 | A quick primer on cross ratios and the anharmonic group | Wild Egg Maths

The cross ratios is a fundamental concept both in affine geometry and projective geometry. Here we give a quick primer, noting some common pitfalls that even advanced geometry texts succumb to, nd introduce the associated anharmonic group, which is a manifestation of the symmetric group S_3 in the form of Mobius transformations which describe all possible cross ratios formed by four collinear points. Along the way we verify our remarkable new cubic identity formed by a kind of Pappus duality. The Playlist for the entire series is called Hexagrammum Mysticum and is available to Members of the Wild Egg Maths channel. Please consider joining to get access to dozens of additional videos! Video Contents: 00:00 Towards Pappus theorem 00:35 A quick primer on the cross ratio 03:57 Definition of cross ratio 08:45 Actual example of a cross ratio 14:37 The anharmonic group ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Wild Egg Maths Playlists (some available only to Members!)    • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist   ************************************************ Here are the Insights into Mathematics Playlists:    • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist   ****************