The Brachistochrone Problem, between Euclidean and Hyperbolic

Year: 2008 Authors: Robert Smits

Core claim

A parameterized family of conformal metrics unifies Euclidean, brachistochrone, and hyperbolic geometries through discrete square models and continuous geodesics.

Topics

discrete conformal geometry, brachistochrone problem, hyperbolic geometry, tilings and patterns, geodesics

Domains

differential geometry, metric geometry, variational calculus, non-Euclidean geometry, wallpaper patterns, Escher, tiling geometry, visual pattern design

Methods

sequence-based square coverings, Snell’s law derivation, conformal metric family, geometric comparison

Media

discrete square diagrams, cycloid curves, printed figures

Source status

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