Half-slope and the full group of Euclidean isometries | WildTrig: Intro to Rational Trigonometry скачать в хорошем качестве

Half-slope and the full group of Euclidean isometries | WildTrig: Intro to Rational Trigonometry

While we may define planar reflections and rotations in terms of points on the unit circle, there is an alternate method which is also useful, using the important idea of the half-slope of such a point. This is intimately connected with the rational parametrization of the unit circle. In this video we recast our algebraic understanding of composition of grounded isometries (i.e. reflections and rotations that fix the origin) in terms of the corresponding half-slopes. This includes introducing the circle sum of half-slopes, and then investigating powers of rotations by means of some remarkable formulas for higher circle sums. Then we move to understanding the full group of isometries by introducing the third kind of isometries: translations. ************************ 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:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   ************************