Affine geometry and barycentric coordinates | WildTrig: Intro to Rational Trigonometry

Affine geometry is the geometry of parallel lines. Using parallelism, we show how to construct a ruled line, how to find the midpoint of a segment, and divide a segment into a given ratio. We connect this to Archimedes law of the lever, and then extend to barycentric coordinates with respect to a triangle. This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry. Video Content: 00:00 Affine geometry and barycentric coordinates 01:20 Affine geometry 01:36 Working on the framework 03:56 The midpoint of a segment 05:40 Balancing masses 09:43 Exercise to determine ratios ************************ 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 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   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   ************************