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The Fibonacci sequence: relationship to the human hand.

Andrew E Park1, John J Fernandez, Karl Schmedders

  • 1Department of Orthopaedic Surgery, Section of Hand and Elbow Surgery, Rush-Presbyterian-St. Luke's Medical Center, Chicago, IL, USA.

The Journal of Hand Surgery
|February 4, 2003
PubMed
Summary

The human hand

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Area of Science:

  • Anatomy
  • Biometrics
  • Biomechanics

Background:

  • The motion path of digits is theorized to follow an equiangular spiral.
  • This implies that human hand bone lengths may approximate the Fibonacci sequence (phi ≈ 1.61803).

Purpose of the Study:

  • To test the hypothesis that metacarpal and phalangeal bone lengths follow the Fibonacci relationship.
  • To investigate the mathematical validity of applying the Fibonacci sequence to human hand anatomy.

Main Methods:

  • Standardized X-rays of 100 healthy volunteers' hands were analyzed.
  • Ratios of adjacent bone lengths (metacarpal, proximal, middle, distal phalanges) were calculated.
  • Confidence intervals were used to assess the presence of the Fibonacci ratio (phi).

Main Results:

  • Only 1 of 12 bone length ratios (small finger metacarpal to proximal phalanx) included phi in its 95% confidence interval.
  • The greatest variability in ratios was observed in the small finger phalanges.
  • The Fibonacci relationship was not consistently found across hand bones.

Conclusions:

  • The mathematical application of the Fibonacci sequence to human hand bone lengths is not supported by this study.
  • Discrepancies may arise from measurement points (joint line vs. center of rotation).

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