ORIGINAL ARTICLE 

Year : 2021  Volume
: 4
 Issue : 1  Page : 5863 

Fibonacci's mathematical sequence predicts functional and actual lengths of the phalanges of the hand
Andrew S Miller, Rhodri Gwyn, Dhritiman Bhattacharjee, Louisa N Banks
Department of Trauma and Orthopaedic, Glan Clwyd Hospital, Bodelwyddan, North Wales, UK
Correspondence Address:
Louisa N Banks Room 27, Ivor Lewis Building, Glan Clwyd Hospital, Sarn Lane, North Wales, LL18 5UJ UK
Source of Support: None, Conflict of Interest: None
DOI: 10.4103/JNSM.JNSM_65_20


Background: Fibonacci described a mathematical sequence starting 0, 1, 1, 2, 3, 5, 8… where each sub sequential number is the sum of the two preceding numbers. The golden ratio (Phi, Φ = 1.618) is the ratio of two consecutive numbers in the sequence. Here, we investigate whether there is a relationship between these mathematical sequences or ratios and functional or actual lengths of the digits. Methods: Two hundred radiographs of the hand were reviewed by three independent reviewers (interobserver correlation r >0.98), and the actual and functional phalangeal lengths were measured. Results: Both the functional and actual lengths of the phalanges of the little finger followed Fibonacci's sequence. The index, middle, and ring fingers followed a mathematical sequence related to the Fibonacci's sequence. We were not able to demonstrate any direct relationship between phalangeal length and the golden ration (Φ). The sum of lengths of the distal and middle phalanx equals the length of the proximal phalanx with great accuracy. Conclusions: This is useful in many surgical situations (congenital deformities, polytrauma to the hands, and arthroplasty).




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