Conformal Maps and Hyperbolic Geometry

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Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Explores Lie groups, scalar fields, and vector spaces transformations.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.

Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Introduces the 5th postulate in Euclidean geometry and explores non-Euclidean geometries and their implications.