Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger скачать в хорошем качестве

Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger

In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is considered as the space of one-dimensional subspaces of a three dimensional vector space, or in other words lines through the origin. In this way we can introduce homogeneous coordinates [X:Y:Z] for the more familiar points [x,y]; the big advantage is that now points at infinity become concrete and accessible: they are simply points of the form [X:Y:0]. A curve like the parabola y=x^2 gets a homogeneous equation YZ=X^2, including now the point at infinity [0:1:0], which corresponds to the direction in the y axis. This gives a uniform view of conics close to Apollonius' view in terms of slices of a cone. We will see that homogeneous coordinates provide a powerful and useful tool to not only the study of conics and algebraic curves in the plane, but also to quadrics and higher algebraic surfaces in space. ************************ 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   ************************