Fibonacci Sequence


About

The Fibonacci sequence is a sequence of numbers (the Fibonacci numbers) in which each number is the sum of the two preceding ones, starting from 0 and 1. That is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 51, ...

These numbers were of interest to D'Arcy because the sequence appears in nature frequently, for example in phyllotaxis and arrangements of pine cones. D'Arcy, for a period, was particularly interested in these numbers in relation to the number of ray flowers of the White Daisy (ms26206). While recovering from broken ribs, Bennett derived a formula, shown below, that he thought might have related to the problem (ms26062) and asked whether the daisy might be "supermodally orchidaceous". In the end, Dorothy Wrinch's pressing marital issues and financial situation drew D'Arcy's attention away from the problem.

formula1
formula2

The numbers also closely relate to the golden ratio, and thus the golden spiral: a logarithmic spiral whose growth factor is the golden ratio.

Spiral
The Golden Spiral
Nature
The Fibonacci Sequence in Nature

Correspondents

Geoffrey Thomas Bennett

Introduction

   

Overview & D'Arcy's Life

   

On Growth and Form

   

Heilmann & Shufeldt

   

Maths of Transformations

   

Correspondence

   

D'Arcy and Mathematics

   

Coordinate Transformations

   

Logarithmic Spirals

   

Forms of Cells

   

Forms and Mechanical efficiency

   

Shrinkage

   

Wartime and D'Arcy

   

The Leg as a Pendulum

   

Recreational Maths

   

Fibonacci Sequence

   

Cell-Aggregates

   

All Correspondence Links

Claxton Fidler

   

Eric Harold Neville

   

John Marshall

   

Alfred North Whitehead

   

Charles Robert Darling

   

Peter Guthrie Tait

   

William Peddie

   

Geoffrey Thomas Bennett

   

Dorothy Wrinch

   


Main Index Biographies Index


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Cammy Sriram and Edward Smith © July 2019
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School of Mathematics and Statistics
University of St Andrews, Scotland

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