Turn angles, continued fractions and approximate geometry | WildTrig: Intro to Rational Trigonometry скачать в хорошем качестве

Turn angles, continued fractions and approximate geometry | WildTrig: Intro to Rational Trigonometry

The natural unit of angle is not the degree, or the radian, or the grad. The natural unit assigns a value of 1 to the full turn around the circle, and we could call this unit turn angle a circ, following a suggestion by a viewer, Vincent Marciante. In this video we explore how to evaluate arbitrary angles in terms of a unit circ, at least approximately, by employing an angular variant of the technology of continued fractions used to measure commensurability of linear segments. Continued fractions arise from the Euclidean algorithm for finding greatest common divisors, and that idea applies just as well to angles as it does to segments. Nevertheless, there is a big difference between discussing commensurability of linear segments and circular arcs: while we can arbitrarily divide a given segment into equal pieces, the same is generally impossible for circular arcs. ************************ 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   ************************