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Fibonacci Numbers - Myths and facts

The main mathematical news

1999:  Discovery of Viswanath’s Constant – The growth rate of every random Fibonacci sequence is equal to 1.1319882….

2000: The mechanism controlling the radial positioning of leaves was found. Auxin, a plant hormone, regulates the maximal distance between blooming buds, and as a result the divergence angle between successive leaves approaches 137.508o – “the golden angle”.

Early 21st century: Debunking myths regarding the golden ratio in human anatomy, architecture, art, etc.

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Additional Theorems / conjectures / Open questions

*    The ratio between successive terms in the Fibonacci sequence tends to a constant number:

*     1843: Jacques Binet published a direct formula for the terms of Fibonacci sequence:

* 1999: The random Fibonacci sequence: t1=t2=1, and each subsequent term is determined by a coin toss:

Ø  Heads – add the previous two terms,

Ø  Tails – subtract the previous term from its predecessor.

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The main mathematical concepts / Principles

Arithmetic

(MSC2010#97F99)

*        Fibonacci sequence

*        golden cut

*        golden ratio

*        irrational number

*        Binet’s formula

*        recursive formula

*        random sequence

Real life mathematics (MSC2010#97F90)

golden angle

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