The fibonacci sequence: Relationship to the human hand

Abstract

Purpose: The motion path of the digits follows the path of an equiangular spiral in which a constant angle is formed by all radial vectors along the curve. This implies that the lengths of the metacarpals, proximal, middle, and distal phalanges approximate a Fibonacci sequence in which the ratio of any 2 consecutive numbers approaches the number 1.61803 (phi). This study tested the hypothesis that the metacarpal and phalangeal bone lengths follow the Fibonacci relationship. Methods: Standardized x-rays were taken of the hands of 100 healthy volunteers. The proximal phalanx length was subtracted from the sum of the lengths of the middle and distal phalanges and the metacarpal length was subtracted from the sum of the lengths of the middle and proximal phalanges. Confidence intervals for the quotients of the measured lengths of the adjacent bones of the hand also were used for statistical analysis. Results: Only 1 of 12 bone length ratios contained the ratio phi in the 95% confidence interval, that of the small finger metacarpal and proximal phalanx. The largest variability was seen in the small finger phalangeal relationships. Conclusion: The application of the Fibonacci sequence to the anatomy of the human hand, although previously accepted, is a relationship that is not supported mathematically. The difference between individual bone lengths as measured at the joint line and the center of rotation of the joints may explain our finding. (J Hand Surg 2003;28A:157–160. Copyright © 2003 by the American Society for Surgery of the Hand.)