Metrical Structure and Curvature of a Parabola - Differential Geometry
Offered By: Insights into Mathematics via YouTube
Course Description
Overview
Explore the concept of metrical structure and curvature in differential geometry, focusing on parabolas. Learn about symmetric bilinear forms in affine and projective settings, and delve into the crucial concept of curvature for parabolas of the form y=ax^2. Discover the connections between metrical structures, quadratic forms, and conics, and gain insights into two-dimensional relativistic geometries. Investigate the relationships between a parabola's focus, center of curvature, radius of curvature, and curvature itself, following Zvi Har'El's parabolic approach.
Syllabus
Introduction
Circles
Three dimensions
Plane
Theorem
Condition
Parabolas
Taught by
Insights into Mathematics
Related Courses
Differential CalculusCEC via Swayam Calculus through Data & Modelling: Integration Applications
Johns Hopkins University via Coursera APEX Calculus - Vector-Valued Functions
Sean Fitzpatrick via YouTube Differential Geometry
Math at Andrews via YouTube Calculus III - Multivariable Calculus - Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization
YouTube