Apparently, both New Scientist, April 18, 1992, p. 18 and Physical Review Letters, 68:2098, show that French physicists have built a physical model which seems to show that ‘Fibonacci spiralling’ is a result of a flower's system of keeping the energy required for the growth of its parts (for example, the seeds) to a minimum. As a student of financial markets I was well aware that Fibonacci numbers were relevant in predicting market price changes but didn't realize that nature contained these correlations as well. It would seem plausible that some research into the use of Fibonacci numbers is in order to find how proteins fold while keeping the energy to a minimum. What think ye?

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when i did my biology degree we did an economics module because a lot of the maths is the same - for example, in both you have to determine the best investment of a finite resource...

I think it's more likely that a corellation is found from the results of the rosetta work rather than because of it though - it could manifest itself at a completely different level to which you're trying to apply it to.

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when i did my biology degree we did an economics module because a lot of the maths is the same - for example, in both you have to determine the best investment of a finite resource...

I think it's more likely that a corellation is found from the results of the rosetta work rather than because of it though - it could manifest itself at a completely different level to which you're trying to apply it to.

It is possible that you are correct. I simply posed the question. However I cannot get over, after reading up more on Fibonacci, how these numbers and ratios correlate to the very large and to the very small things in nature, from leaves, petals, DNA, the orbital times of the planets in our solar system, even how rabbits multiply! Here are some interesting quotes to consider followed by their sources. Enjoy, I sure did.

Not only do we discover this pattern in leaf arrangements, but it is also commonly found in the arrangement of many flower petals. Examples: a lily has
3 petals, yellow violet 5, delphinium 8, mayweed 13, aster 21, pyrethrum 34, helenium 55, and michaelmas daisy 89. (my addition..these are all fib. numbers)

When we realize that the information to produce these spirals and numbers in living things is stored in the DNA, should we then be surprised to find that the DNA molecule is 21 angstroms in width and the length of one full turn in its spiral is 34 angstroms, both Fibonacci numbers? The DNA molecule is literally one long stack of golden rectangles. (my addition..a 'golden rectangle' is a rectangle with two sides being = 1 and the other sides = 1.618)

Let's look into the area of very small and very large things. In the world of atoms there are four fundamental asymmetries (structure of atomic nuclei, distribution of fission fragments, distribution of numbers of isotopes, and the distribution of emitted particles), and it is significant that "the numerical values of all of these asymmetries are equal approximately to the `golden ratio,' and that the number forming these values are sometimes Fibonacci or `near' Fibonacci numbers." In changing states of a quantity of hydrogen atoms, as the atoms gain and lose radiant energy at succeeding energy levels, the changing proportion of the histories of the atomic electrons form Fibonacci numbers.

In the area of very large phenomena when the time period of each planet's revolution around the sun is compared in round numbers to the one adjacent to it, their fractions are Fibonacci numbers! Beginning with Neptune and moving inward toward the sun, the ratios are 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, 13/34. These are the same as the spiral arrangement of leaves on plants!

Sources: Marl Wahl, A Mathematical Mystery Tour, Zephry Press, Tucson, AZ. 1988, p. 128.
J. Wlodarski, "The Golden Ratio and the Fibonacci Numbers in the World of Atoms," Fibonacci Quarterly, December 1963, p. 61.
H. E. Huntley, "Fibonacci and the Atom," Fibonacci Quarterly, December 1969, pp. 523_524.
There is still controversy as to whether Pluto is a real planet. Whether or not it is, its distance from Neptune is still a Fibonacci ratio, even if in the opposite direction.

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And of course the golden ration 1 : 1.618 is what you approach when you divide a fibonacci number with its predecessor.

55/34 = 1.6176
89/55 = 1.6181
144/89 = 1.6179

And so on ;)

From what I heard when the ratio is applied to music (frequency of sounds, maybe? I don't remember exactly) it also produces something that is commonly found pleasing.

Definitely more than just a coincidence, no doubt.

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Not only do we discover this pattern in leaf arrangements, but it is also commonly found in the arrangement of many flower petals. Examples: a lily has
3 petals, yellow violet 5, delphinium 8, mayweed 13, aster 21, pyrethrum 34, helenium 55, and michaelmas daisy 89. (my addition..these are all fib. numbers)

The spiral arrangements of pinecones, pineapples, and sunflowers display more than one Fibonacci number at a time, depending on which direction you follow the spiral.

When we realize that the information to produce these spirals and numbers in living things is stored in the DNA, should we then be surprised to find that the DNA molecule is 21 angstroms in width and the length of one full turn in its spiral is 34 angstroms, both Fibonacci numbers? The DNA molecule is literally one long stack of golden rectangles. (my addition..a 'golden rectangle' is a rectangle with two sides being = 1 and the other sides = 1.618)

The angstrom is an arbitrary unit (1 Å = 10^–10 m), so looking for significance in the measurements themselves smacks of numerology. However, their ratio is independent of the units chosen. If you were to look down the axis of a DNA double-helix you’d see that it has decagonal symmetry, so it’s not surprising to find golden-section proportions there.

From what I heard when the ratio is applied to music (frequency of sounds, maybe? I don't remember exactly) it also produces something that is commonly found pleasing.

Not in any obvious way: two pitches with frequencies in the golden ratio make a rather unpleasant-sounding chord about halfway between a minor sixth and a major sixth. (In the well-tempered scale those intervals have frequencies respectively 1.5874 and 1.6818 times that of the tonic.)

If you’re as easily amused as I am ;) you might enjoy this calculator exercise:

1. Key 1;
2. Key +, 1, =, √;
3. Repeat step 2 until bored.

For another, try the same thing but replace the ‘main loop’ with:

2. Key 1/x, +, 1, =.