Media Summary: The commutator of components of the covariant derivative is computed and shown to be proportional to the Gaussian curvature. (November 1, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he ... For information on the visualization please read the note at the end. Few musical works are as loved and as often performed as ...
Classicaldiffgeo Lec 6 B - Detailed Analysis & Overview
The commutator of components of the covariant derivative is computed and shown to be proportional to the Gaussian curvature. (November 1, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he ... For information on the visualization please read the note at the end. Few musical works are as loved and as often performed as ... Streams, Part 2 Despite the copyright notice on the screen, this course is now offered under a Creative Commons license: ... The geodesic curvature of a curve embedded on a surface is related to the curve's turning angle. This observation leads to a ... The second fundamental form is shown to indicate how fast a surface deviates from its tangent plane, generalizing the idea from ...
Bach turns things upside down in this 'Brandenburg' Concerto No. The geodesic deviation is introduced and illustrated on a sphere and a simple differential equation for the evolution of the ... The Poincare Disk model of hyperbolic geometry is introduced. it is mapped onto the Upper Half Plane model of hyperbolic ... (November 9, 2009) Leonard Susskind gives the Surfaces of Revolution. The Torus is introduced and is given a natural coordinate mesh. Its first and second fundamental forms ... Gauss' Theorem Egregium is derived showing that the Gaussian curvature is determined just in terms of a surface's metric and its ...
