Meusnier, Monge and Dupin I | Differential Geometry 31 | NJ Wildberger скачать в хорошем качестве

Meusnier, Monge and Dupin I | Differential Geometry 31 | NJ Wildberger

This is the first of three videos that discuss the mathematical lives and works of three influential French differential geometers. We begin with J. Meusnier, who was a soldier, engineer and mathematician. He investigated lines of curvature and discovered a famous result that shows how to compute the sectional curvature of a surface cut by a non-normal plane, which we restate using the language of Rational Trigonometry--of course! We discuss also elliptic, hyperbolic and parabolic points and umbilic points. Video Contents: 00:00 Introduction 00:59 J.B Meusnier 1754-1793 03:34 Euler - normal curvatures had a maximum value in two per .Directions 07:15 Asymptotic directions 07:46 Center of curvature 09:40 One of principal curvatures 16:30 Umbilic point 18:00 An Ellipsoid with unequal axes 29:47 Proof- (Assumption) 41:19 Recall: Parabola ************************ 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   ************************