Skip to main content

Celtic Knotwork: Mathematical Art

  • Chapter
Mathematical Conversations
  • 1215 Accesses

Abstract

The interlaced ornament produced by Celtic scribes and stone masons has fascinated people for many centuries. The designs, ranging from small individual knots to elaborate panels composed of many motifs, provide the geometrically minded mathematician with a rich source of examples. Many aspects of the interlaced patterns can be studied mathematically, and some of these are explored in this article. We begin with the geometry of the knots.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J. Romilly Allen, Celtic Art in Pagan and Christian Times, London: Methuen (1904).

    Google Scholar 

  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. B. Grünbaum and G. C. Shephard, Tilings and Patterns, New York: Freeman (1987).

    MATH  Google Scholar 

  4. W. W. Menasco, Closed incompressible surfaces in alternating knot and link complements. Topology 23 (1984), 37–44.

    Article  MathSciNet  MATH  Google Scholar 

  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

  • G. Bain, Celtic Art: the methods of construction, London: Constable (1977).

    Google Scholar 

  • I. Bain, Celtic Knotwork, London: Constable (1986).

    Google Scholar 

  • A. Meehan, Celtic Design: knotwork, London: Thames and Hudson (1991).

    Google Scholar 

Related Topics

  • H. Arneberg, Norwegian Peasant Art: men’s handicrafts, Oslo: Fabritius & Son (1951).

    Google Scholar 

  • K. M. Chapman, The Pottery of San Ildefonso Pueblo, School of American Research, monograph 28, Albuquerque: University of New Mexico Press (1970).

    Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • B. Grünbaum, Periodic ornamentation of the fabric plane: lessons from Peruvian fabrics. Symmetry 1 (1990), 48–68.

    Google Scholar 

  • B. Grünbaum and G. C. Shephard, The geometry of fabrics, Geometrical Combinatorics (F. C. Hol-royd and R. J. Wilson, eds), Pitman (1984), 77–97.

    Google Scholar 

  • B. Grünbaum and G. C. Shephard, Interlace patterns in Islamic and Moorish art, Leonardo (1993).

    Google Scholar 

  • B. Grünbaum, Z. Grünbaum, and G. C. Shephard, Symmetry in Moorish and other ornaments, Comp. & Maths. with Appls., vol 12B, Nos. 3/4 (1986), 641–653.

    Article  Google Scholar 

  • A. Hamilton, The art workmanship of the Maori race in New Zealand, Wellington: New Zealand Institute (1896).

    Google Scholar 

  • I. Hargittai and G. Lengyel, The seven one-dimensional space-group symmetries in Hungarian folk needlework, J. Chem. Educ. 61 (1984), 1033.

    Article  Google Scholar 

  • G. H. Knight, The geometry of Maori art. Part I: rafter patterns, New Zealand Math. Mag. (3) 21 (1984), 36–40.

    MathSciNet  Google Scholar 

  • G. H. Knight, The geometry of Maori art. Part 2: weaving patterns, New Zealand Math. Mag. (3) 21 (1984), 80–86.

    MathSciNet  Google Scholar 

  • D. K. Washburn and D. W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, Seattle: University of Washington Press (1988).

    MATH  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Cromwell, P.R. (2001). Celtic Knotwork: Mathematical Art. In: Mathematical Conversations. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0195-0_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0195-0_27

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6556-6

  • Online ISBN: 978-1-4613-0195-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics