The Mathematical Intelligencer

, Volume 15, Issue 1, pp 36–47 | Cite as

Celtic knotwork: Mathematical art

  • Peter R. Cromwell


Symmetry Group Mirror Plane Symmetry Type Incompressible Surface Frieze Pattern 
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  1. 1.
    J. Romilly Allen,Celtic Art in Pagan and Christian Times, London: Methuen (1904).Google Scholar
  2. 2.
    E. H. Gombrich,The Sense of Order: a study in the psychology of decorative art, Ithaca, NY: Cornell University Press (1979).Google Scholar
  3. 3.
    B. Griinbaum and G. C. Shephard,Tilings and Patterns, New York: Freeman (1987).Google Scholar
  4. 4.
    W. W. Menasco, Closed incompressible surfaces in alternating knot and link complements.Topology 23 (1984), 37–14.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    A. V. Shubnikov and V. A. Koptsik,Symmetry in Science and Art (translated from the Russian by G. D. Archard), New York: Plenum (1974).Google Scholar

Further Reading Celtic Knotwork

  1. G. Bain,Celtic Art: the methods of construction, London: Constable (1977).Google Scholar
  2. I. Bain,Celtic Knotwork, London: Constable (1986).Google Scholar
  3. A. Meehan,Celtic Design: knotwork, London: Thames and Hudson (1991).Google Scholar

Related Topics

  1. H. Arneberg,Norwegian Peasant Art: men’s handicrafts, Oslo: Fabritius & Son (1951).Google Scholar
  2. K. M. Chapman,The Pottery of San Ildefonso Pueblo, School of American Research, monograph 28, Albuquerque: Uni-versity of New Mexico Press (1970).Google Scholar
  3. D. W. Crowe and D. K. Washburn, Groups and geometry in the ceramic art of San Ildefonso,Algebras, Groups and Geometries (2) 3 (1985), 263–277.MathSciNetGoogle Scholar
  4. B. Grunbaum, Periodic ornamentation of the fabric plane: lessons from Peruvian fabrics.Symmetry 1 (1990), 48–68.Google Scholar
  5. B. Grunbaum and G. C. Shephard, The geometry of fabrics,Geometrical Combinatorics (F. C. Holroyd and R. J. Wil- son, eds), Pitman (1984), 77-97.Google Scholar
  6. B. Grunbaum and G. C. Shephard, Interlace patterns in Is- lamic and Moorish art,Leonardo (in press).Google Scholar
  7. B. Grunbaum, Z. Grunbaum, and G. C. Shephard, Symme- try in Moorish and other ornaments,Comp. & Maths, with Appls., vol 12B, Nos. 3/4 (1986), 641–653.CrossRefMathSciNetGoogle Scholar
  8. A. Hamilton,The art workmanship of the Maori race in New Zealand, Wellington: New Zealand Institute (1896).Google Scholar
  9. I. Hargittai and G. Lengyel, The seven one-dimensional space-group symmetries in Hungarian folk needlework,J. Chem. Educ. 61 (1984), 1033.CrossRefGoogle Scholar
  10. G. H. Knight, The geometry of Maori art. Part I: rafter pat- terns, New Zealand Math. Mag. (3) 21 (1984), 36–40.MathSciNetGoogle Scholar
  11. G. H. Knight, The geometry of Maori art. Part 2: weaving patterns,New Zealand Math. Mag. (3) 21 (1984), 80–86.MathSciNetGoogle Scholar
  12. D. K. Washburn and D. W. Crowe,Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, Seattle: University of Washington Press (1988).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1993

Authors and Affiliations

  • Peter R. Cromwell
    • 1
  1. 1.Department of Pure MathematicsThe University of LiverpoolLiverpoolEngland

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