Through Mazes to Mathematics

References

V. I. Arnol'd, A branched covering of CP^2 --> S^4 , hyperbolicity and projectivity topology, Siberian Math. Journal 717-725 (translated from Sibirskii Matematicheskii Zhurnal , Vol. 29, No. 2, pp. 36-47, September-October 1988)

Janet Bord, Mazes and Labyrinths of the World, Latimer, London 1976

Marilyn Clark, British turf labyrinths -- an update.

P. Di Francesco, O. Golinelli and E. Guitter, Meanders: exact asymptotics, Nucl. Phys. B 570 (2000) 699-712; preprint available online.

Penelope Reed Doob, The Idea of the Labyrinth, Cornell, Ithaca and London 1990

J. Harer and D. Zagier, The Euler charcteristic of the moduli space of curves, Invent. Math. 85 (1986) 457-485

M. G. Harris, A diagrammatic approach to the meander problem, (1998), preprint available online.

I. Jensen and A. J. Guttmann, Critical exponents of plane meanders, J. Phys. A 33 (2000) L187-L192; also available online.

Hermann Kern, Labyrinthe (2nd ed.) Prestel-Verlag, München 1983 [an expanded version of] Labirinti. Forme e interpretazioni. 5000 anni di presenza di un archetipo. Feltrinelli, Milano 1981
NOTE: An English edition is now available: Through the Labyrinth: Designs and Meanings over 5,000 Years. Edited by Robert Ferré and Jeff Saward. Translated from the German by Abigail H. Clay with Sandra Burns Thomson and Kathrin A. Velder. Various chapter addenda by Jeff Saward. An appended chapter, "The Labyrinth Revival," by Robert Ferré. Munich: Prestel Verlag, 2000. ISBN: 3-7913-2144-7. Hardback.

John E. Koehler, S.J., Folding a strip of stamps, J. Combinatorial Th. 5 (1968) 135-152

S. K. Lando and A. K. Zvonkin, Meanders, Selecta Mathematica Sovietica Vol. 11, No. 2 (1992) 117-144

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science 117 (1993) 227-241

Gilbert Levitt and Harold Rosenberg, Differentiability and topology of labyrinths in the disc and annulus, Topology 26 (1987) 173-186

W. H. Matthews, Mazes and Labyrinths, a General Account of their History and Developments, Longmans, Green, London 1922; reissued by Singing Tree Press, Detroit 1969; and by Dover

Th. Motzkin, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products, Bull. Amer. Math. Soc. 54 (1948) 352-360

Anthony Phillips, The topology of Roman mosaic mazes, Leonardo 23 (1992) 321-329 (reprinted in Michele Emmer, ed., The Visual Mind: Art and Mathematics, MIT Press 1993, 65-73)

Harold Rosenberg, Labyrinths in the disc and surfaces, Ann. Math. 117 (1983) 1-33

P. Rosenstiehl, How the ``Path of Jerusalem" in Chartres separates birds from fishes, in: M. Emmer et al. eds., M. C. Escher: Art and Science, North Holland, Amsterdam, New York, Oxford, Tokyo, 1987, pp. 221-230.

N. J. A. Sloane, On-Line Encyclopedia of Integer Sequences, sequence A005316

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications, Proc. 1998 SETA conf., ed. C. Ding, T. Helleseth and H. Niederreiter, Springer-Verlag, 1999, pp. 103-130; preprint available online.

Warren Smith, Studies in Computational Geometry Motivated by Mesh Generation, Thesis, Princeton 1988.

Bo Stjernström, Dokumentation och klassificering av labyrinter, Bottnisk Kontakt I, Skrifter fran Örnsköldsviks museum nr 1 (1982) 101-112

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January 16 2001