The Brachistochrone Problem between Euclidean and Hyperbolic

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Reference

Robert Smits: The Brachistochrone Problem between Euclidean and Hyperbolic. In: Bridges 2008. Pages 87–92

DOI

Abstract

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.

Extended Abstract

Bibtex

Used References

[1] P.-G. de Gennes, Simple Views on Condensed Matter. World Scientific Publishing Company, 1998.

[2] P. Dombrowski, The Brachistochrone Problem: a Problem of Elementary Differential Geometry, Geometry and topology of submanifolds, VIII pp. 148-167 World Scientific Publishing Co. 1996

[3] R. Ferreol and J. Mandonnet, Courbe Brachistochrone at http://www.mathcurve.com/

[4] J. Hawkins, On Intelligence, Holt Paperbacks 2005

[5] R. Smits, Square Decompositions with Hyperbolic Consequences in Art, Chemical Physics and Mathematics, Bridges Proceedings 2003


Links

Full Text

http://archive.bridgesmathart.org/2008/bridges2008-87.pdf

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http://archive.bridgesmathart.org/2008/bridges2008-87.html