The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b скачать в хорошем качестве

The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b

Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine space of one higher dimension. Thus the projective line is viewed as the space of lines through the origin in two dimensional space, while the projective plane deals with one dimensional and two dimensional subspaces of a 3 dimensional affine xyz space (called respectively projective points and projective lines). This relates to Renassiance artists attempts to render perspectives correctly; we illustrate by looking at a parabola in a somewhat novel way. The usual two dimensional view of the projective plane emerges by intersecting with the plane z=1 in the ambient x,y,z space. This way the circle is the two dimensional representation of a cone: a view relating back to the ancient Greeks. For more information on projective geometry, see WT31-WT41 in my WildTrig series. CONTENT SUMMARY: 2 dimensional geometry the arena of hyperbolic geometry @00:12 page change: adopting a viewing plane @08:07 The circle in projective homogeneous coords.(very important picture in mathematics and physics: special relativity) at the heart of hyperbolic geometry @16:14 ************************ 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   ************************