Metrical Structure and Curvature of a Parabola - Differential Geometry

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.