The Brachistochrone Problem between Euclidean and Hyperbolic

Robert Smits
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008)
Pages 87–92


We investigate discrete models of the upper-half plane endowed with various conformal metrics, which in essence are intermediaries between the standard Euclidean and the hyperbolic ones. The brachistochrone problem is related to a metric associated to arithmetic sequences.