Fibonacci spiral cactus6/24/2023 ![]() ![]() 1932, then I'll have to redefine my notion of "modern times". The effect of isolating a primordium" (Philosophical Transactions of the Royal Society of London), which was published in. if the author meant Richard and Mary Snow's papers, like "Experiments on phyllotaxis. They're still active, so it might happen. I've requested the person who added it provide a citation. InAJar 16:39, 28 February 2007 (UTC) Reply Yes, it's annoying when you see that sort of thing. That way, people could read more about the research being done on this topic. ![]() ![]() Who are "Snow and Snow"? I think that the article ought to cite this. "In modern times, researchers such as Snow and Snow have continued these lines of inquiry." Chiswick Chap ( talk) 08:32, (UTC) Reply I note that you've joined a discussion that is more than 10 years old! There might be a hint in that figure. The mathematics of Fibonacci is not in dispute, but its applicability to plant biology is - the presence of spirals does not prove that a particular mathematical approach is the right one. It is probably adequately covered on this page already. Froszthamr ( talk) 08:03, (UTC) Reply You are right that it is controversial, because it has been taken up for non-mathematical reasons and made too much of, on this and other pages, supported by unreliable sources. I am a computer science/maths student, so naturally have a strong love of them, along with the study of fractals, another area in which the Golden Ratio pops up. If anyone else is interested, I'd be happy to supplement the information with a lot that I have, although I thought it better to ask first on the Talk page, as there is a small number of people (that I'm aware of, at least) who would ironically find any discussion of the Golden Ratio "controversial". Dominus 14:34, (UTC) I don't know what anyone else thinks, but I personally am grateful to you for including all the useful and interesting information on the Golden Ratio and its abundance in nature-in this case in the study of phyllotaxy. So it seems clear that the appearance of φ here is not a coincidence, because plants that distribute their leaves with the 360/φ angle will tend to outcompete plants that distribute their leaves in some other way, and the closer the plant can get to the uniform 360/φ angle, the more successful it will tend to be. Leaf placement is more favorable for certain angles than for other angles, and the optimal leaf placement is achieved when the angle is 360/φ. The distribution of leaves on the stem is one of these, because there's a simple mechanism that leads to favorable leaf placement. Other appearances of φ, however, are not coincidences there will be some reason why they appear, and when the number that is actually measured differs from φ, we can view that as a deviation. Maybe it is about three-fifths of the way up, but there's no reason to identify that 3/5 with anything related to φ. For example, is your navel really 1/φ of the way up your body? Not so far as anyone can tell. Some of these are coincidences, where it seems that there is no particular reason why it should be 1.6 rather than 1.7 or 1.5 or 23. There are going to be a lot of appearances of φ in the world. I'm new but having read Talk:Fibonacci number/Phyllotaxis, I don't know why the arrangement of leaves on a stalk isn't just one more example of those things that are. ![]() Some of it might be useful here once this article is fleshed out a little more. I put some discssuion of the appearance of Fibonacci numbers and the golden ratio in phyllotaxis at Talk:Fibonacci number/Phyllotaxis. ![]()
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