- Snapshots of modern mathematics
- Pierre de Fermat and Andrew Wiles in Czech Republic stamps
- Stefan Banach (March 30, 1892 – August 8, 1945)
- Guessing the Numbers
- What is mathematics for Ehrhard Behrends
- What is mathematics for Krzysztof Ciesielski
- The Three Ducks Trick
- What is mathematics for Franka Brueckler
Turing, Fibonacci and the sunflowers
Article previously published on Doc Madhattn. June 23, 2017: Happy Alan Turing 105th Birthday!
One of the last Alan Turing‘s work is about Fibonacci numbers in nature:
One of a number of problems [Alan Turing] was trying to solve was the appearence of Fibonacci numbers in the structure of plants.[1]Swinton J. (2004). Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis, Alan Turing: Life and Legacy of a Great Thinker, 477-498. DOI: 10.1007/978-3-662-05642-4_20 (pdf)
The problem was knwon as the Fibonacci phyllotaxis, and we can state it in this way:
the spiral shapes on the heads of sunflowers seemed to follow the Fibonacci sequence, prompting [Turing’s] proposal that by studying sunflowers we might better understand how plants grow
A sunflower with Fibonacci’s spiral
Turing wrote his interest in a letter to the zoologist JZ Young:
About the point (iii) Turing wrote in another letter:
Our new machine is to start arriving on Monday. I am hoping to do something about ‘chemical embyology’. In particular I think I can account for the appearence of Fibonacci numbers in connection with fir-cones.[2]See note 1.
In 2012, Jonathan Swinton, during the Manchester Science Festival, announced the results of the great experiment about the Turing’s sunflower:
And finally results are published last year on Royal Society open science[3]Swinton, J., Ochu, E., & MSI Turing’s Sunflower Consortium. (2016). Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment. Royal Society open science, 3(5), 160091. doi:10.1098/rsos.160091: a great result for Alan Turing and citizen science!
References
| 1. | ↑ | Swinton J. (2004). Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis, Alan Turing: Life and Legacy of a Great Thinker, 477-498. DOI: 10.1007/978-3-662-05642-4_20 (pdf) |
| 2. | ↑ | See note 1. |
| 3. | ↑ | Swinton, J., Ochu, E., & MSI Turing’s Sunflower Consortium. (2016). Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment. Royal Society open science, 3(5), 160091. doi:10.1098/rsos.160091 |
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