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Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis?

TODD J. COOKE
2006 Botanical journal of the Linnean Society  
This paper reviews the fundamental properties of number sequences, and discusses the under-appreciated limitations of the Fibonacci sequence for describing phyllotactic patterns.  ...  A favourite botanical example is the apparent relationship between phyllotaxis (i.e. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci  ...  ACKNOWLEDGEMENTS This paper is dedicated to my friend Don Kaplan on the occasion of his retirement from the University of California, Berkeley.  ... 
doi:10.1111/j.1095-8339.2006.00490.x fatcat:mosywkas6zaprny3hln34elppq

Non-functional biomimicry: utilizing natural patterns in order to provoke attention responses

Bryan G. Young, Andrew Wodehouse
2016 International Journal of Design Creativity and Innovation  
Natural reoccurring patterns arise from chaos and are prevalent throughout nature. The formation of these patterns is controlled by, or produces, underlying geometrical structures.  ...  The results showed that the underlying geometry of natural patterns has the potential to induce attention responses to a statistically significant level.  ...  Acknowledgements The authors would like to thank Kim Williams for proofreading the document. Ball, P., & Borley, N. R. (1999). The self-made tapestry: pattern formation in nature (Vol. References  ... 
doi:10.1080/21650349.2016.1246204 fatcat:x5xjgcj2dbcrxp3vf3z7xix64i

Page 236 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
One property of triangular numbers. 2000b:11013 Drobot, Vladimir On primes in the Fibonacci sequence. 2000i:11031 Dunlap, Richard A. * The golden ratio and Fibonacci numbers. 2000j:11021 Elia, Michele  ...  On general divisibility of sums of integral powers of the golden ratio. (see 2000j:11003) — (with Filipponi, Piero) Division of Fibonacci numbers by k. 2000c:11022 Gould, Henry W.  ... 

The Golden Relationships: An Exploration of Fibonacci Numbers and Phi

Anthony Watson, Anthony Watson
2017 unpublished
The Greek letter Ø (Phi), represents one of the most mysterious numbers (  ...  Acknowledgements This project was made possible through the support of many people to whom I owe a debt of gratitude. I first want to thank the wonderful staff and faculty of GLS for all the support  ...  In his book, The Golden Ratio and Fibonacci Numbers, Richard Debnath explains the derivation of the Golden Ratio as: In geometry, the golden ratio (or the golden number or the golden section) is defined  ... 
fatcat:limf6l4zmrclvid2s557lhr2ju

Wearing tone-coloured glasses: a 'colour-first' compositional approach to the modern wind band [article]

Jodie Blackshaw, University, The Australian National, University, The Australian National
2020
Ongoing studies into the creative and compositional process conducted by social psychologists and musicologists are reviewed, revealing the impact of early interactions with music and music education on  ...  Research into my own compositional process is conducted and a set of questions on "how composers compose", devised by Dr.  ...  The emotional journey, that is inherent in the poem, governs the structure of the third movement: Measures 1-12 Measures 13  ... 
doi:10.25911/5ed77c968b164 fatcat:rmg5m2nmqvaqhgvqkyh2ovzq4u