Hi guys, Welcome to the Advanced Video Search Engine, and you are watching The Real Projective Plane. That video is uploaded by bothmer at 2006-12-02T13:57:27-08:00. We are promoting this video only for entertainment and educational purpose only. So, I hope you like & enjoy it. [lDqmaPEjJpk]
| Name | The Real Projective Plane |
| Video Uploader | Video From bothmer |
| Upload Date | This Video Uploaded At 02-12-2006 21:57:27 |
| Video Discription | The projective plane is the space of lines through the origin in 3-space. In the projective plane, we have the remarkable fact that any two distinct lines meet in a unique point. Moreover, we may not distinquish between different kinds of smooth conic sections, e.g. between an ellipse and a hyperbola, as illustrated by the animation. Notice that to each line through the origin correspond two antipodal points of a sphere which is centered at the origin. Instead of looking at the lines in total, we may thus restrict ourselves to the points on the sphere. Here, a line becomes a great circle and it is clear that any two such circles meet in a unique pair of antipodal points. Similarly, we may see that a hyperbola is projectively the same thing as an ellipse. Going back to the definition: They are both just a cone in 3-space; each line on the cone is one projective point of the projective conic section. This animation was made by Oliver Labs using surfex. This animation was #3 on our geometric animations advent calendar: http://www.calendar.algebraicsurface.net lDqmaPEjJpk |
| Category | Howto & Style |
| Tags | geometry | mathematics | projective | plane | conic | section | advent | calendar | bothmer | hannover | oliverlabs | saarbruecken | surfex | cg |
