Skip to main content
SpringerLink
Log in

Fibonacci, Littler, and the Hand: A Brief Review

  • Review Articles of topics
  • Published:
HAND

Abstract

In a landmark paper published in 1973, the eminent hand surgeon J. William Littler, MD, proposed two mathematical relationships between the anatomic and functional geometry of the hand. His proposal that the motion of the tips of the fingers follow an equiangular spiral has been experimentally supported. Studies have not supported his other idea that the lengths of the phalanges follow a Fibonacci series. This review, after providing the necessary mathematical background, reexamines Littler's claims, presents the associated studies, and re-evaluates their conclusions. Our analysis shows that the functional lengths of the phalanges of the little finger actually do follow a Fibonacci series and that the functional lengths of the index, long, and ring fingers follow a mathematical relative of the Fibonacci series.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Bashour M. An objective system for measuring facial attractiveness. Plast Reconstr Surg. 2006;118(3):757–74. discussion 775-6.

    Article  CAS  PubMed  Google Scholar 

  2. Bashour M. History and current concepts in the analysis of facial attractiveness. Plast Reconstr Surg. 2006;118(3):741–56.

    Article  CAS  PubMed  Google Scholar 

  3. Dumont C et al. Morphology of the interphalangeal joint surface and its functional relevance. J Hand Surg [Am]. 2008;33(1):9–18.

    Article  Google Scholar 

  4. Dumont C et al. Quantified contours of curvature in female index, middle, ring, and small metacarpophalangeal joints. J Hand Surg [Am]. 2009;34(2):317–25.

    Article  Google Scholar 

  5. Garland TK. Charity, math and music—harmonious connections. White Plains, NY: Dale Seymore Publications; 1995.

    Google Scholar 

  6. Gullberg J. Mathematics: from the birth of numbers. New York: W.W. Norton & Company, Ltd; 1997.

    Google Scholar 

  7. Gupta A et al. The motion path of the digits. J Hand Surg [Am]. 1998;23(6):1038–42.

    Article  CAS  Google Scholar 

  8. Hamilton R, Dunsmuir RA. Radiographic assessment of the relative lengths of the bones of the fingers of the human hand. J Hand Surg [Br]. 2002;27(6):546–8.

    CAS  Google Scholar 

  9. Huntley HE. The divine proportion: a study in mathematical beauty. New York, NY: Dover Publications; 1970.

    Google Scholar 

  10. Koshy T. Fibonacci and Lucas numbers with applications. New York: Wiley-Interscience; 2001.

    Google Scholar 

  11. Lawrence T, Trail IA, Noble J. Morphological measurements of the proximal interphalangeal joint. J Hand Surg [Br]. 2004;29(3):244–9.

    CAS  Google Scholar 

  12. Littler JW. On the adaptability of man's hand (with reference to the equiangular curve). Hand. 1973;5(3):187–91.

    Article  CAS  PubMed  Google Scholar 

  13. Markley JM. The Fibonacci sequence: relationship to the human hand. J Hand Surg [Am]. 2003;28(4):704–6. author reply 706.

    Article  Google Scholar 

  14. Marzke MW, Marzke RF. Evolution of the human hand: approaches to acquiring, analysing and interpreting the anatomical evidence. J Anat. 2000;197(Pt 1):121–40.

    Article  PubMed  Google Scholar 

  15. McCarthy JG. J. William Littler, M.D., 1915 to 2005. Plast Reconstr Surg. 2006;118(6):1504–5.

    Article  CAS  Google Scholar 

  16. Park AE et al. The Fibonacci sequence: relationship to the human hand. J Hand Surg [Am]. 2003;28(1):157–60.

    Article  Google Scholar 

  17. Ricketts RM. Divine proportion in facial esthetics. Clin Plast Surg. 1982;9(4):401–22.

    CAS  PubMed  Google Scholar 

  18. Seghers MJ, Longacre JJ, deStefano GA. The golden proportion and beauty. Plast Reconstr Surg. 1964;34(4):382–6.

    Article  Google Scholar 

  19. Tamai K et al. Three-dimensional geometric analysis of the metacarpophalangeal joint. J Hand Surg [Am]. 1988;13(4):521–9.

    Article  CAS  Google Scholar 

  20. Thompson DAW. On growth and form. Cambridge [Eng.]: University Press; 1942.

    Google Scholar 

  21. Tucker VA. The deep fovea, sideways vision and spiral flight paths in raptors. J Exp Biol. 2000;203(Pt 24):3745–54.

    CAS  PubMed  Google Scholar 

  22. Vegter F, Hage JJ. Clinical anthropometry and canons of the face in historical perspective. Plast Reconstr Surg. 2000;106(5):1090–6.

    Article  CAS  PubMed  Google Scholar 

  23. Weisstein EW. Lucas sequence. MathWorld: A Wolfram Web Resource Volume; 2008.

    Google Scholar 

  24. Zhang X, Lee SW, Braido P. Determining finger segmental centers of rotation in flexion–extension based on surface marker measurement. J Biomech. 2003;36(8):1097–102.

    Article  PubMed  Google Scholar 

Download references

Acknowledgement

The authors would like to thank John M. Markley, Jr., MD, for his assistance in understanding the mathematical concepts and his support.

Author information

Authors and Affiliations

  1. Yale University, PO Box 205869, New Haven, CT, 06520-5869, USA

    Alan L. Hutchison

  2. Michigan State University, 2300 E. 30th Street, Building B, Suite 103, Farmington, NM, 87401, USA

    Richard L. Hutchison

Authors
  1. Alan L. Hutchison
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard L. Hutchison
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard L. Hutchison.

About this article

Cite this article

Hutchison, A.L., Hutchison, R.L. Fibonacci, Littler, and the Hand: A Brief Review. HAND 5, 364–368 (2010). https://doi.org/10.1007/s11552-010-9268-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11552-010-9268-6

Keywords

Search

Navigation