Wikipedia:Reference desk/Archives/Mathematics/2024 April 23

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April 23

Fibonacci numbers and pineapples

The article on Fibonacci numbers mentions the pineapple, but I am unable to discover when, in the literature, this was first discussed. Later in the aforementioned article it states, "In 1830, K. F. Schimper and A. Braun discovered that the parastichies (spiral phyllotaxis) of plants were frequently expressed as fractions involving Fibonacci numbers." Given that the discussion of pineapples was extremely popular at this time in the early 19th century, one would expect it to be found within that time frame. However, I cannot find anything until the mid to late 20th century, possibly starting with Onderdonk 1970. Does anyone know when Fibonacci numbers were first discussed in reference to the pineapple, and if it was before the 20th century? As it stands, 1830 would fit absolutely perfectly into the pineapple timeline I'm working on, but I can find no supporting evidence for this idea. Viriditas (talk) 23:17, 23 April 2024 (UTC)

Pineapples are mentioned as an example in a long list of diverse plant species. In other words there's nothing specifically notable about pineapples in relation to Fibonacci numbers. Further on the article also mentions daises and the image shows a chamomile. I think the reason pineapples are mentioned is because someone was able to find a citation for them, and perhaps also because many people can find them in their local supermarket. I remember counting rows on a teasel flower head and coming up with Fibonacci related numbers, but I doubt it's mentioned a lot in the literature. It seems to be a general property of Phyllotaxis, or the way plants grow, though there are exceptions, and the "Repeating spiral" section of that article mentions more about Fibonacci numbers. The article mentions Kepler having pointed out the presence of Fibonacci numbers in nature; that was 400 years ago. I don't know if Kepler ever saw a pineapple though. --RDBury (talk) 02:02, 24 April 2024 (UTC)

Yes, I’m aware of that. What’s notable in this context is that pineapples were introduced to Europe and it led to a great deal of interest. I’m tying to trace the discussion of pineapples throughout each discipline as it arose within a specific 150 year time frame of interest before cultivation and mechanization led to wider availability of the fruit. One of the reasons so many different disciplines discussed pineapples is because they were considered new, difficult to impossible to grow in cold climates, and didn’t have a previous known history in Europe, giving rise to people in different fields using them as examples in their domain-specific literature. It would be kind of like talking about the Internet in your field of expertise in the 1990s. It was somewhat new and different for the general public and people were trying to apply it to their knowledge base. For example, both Leibniz and Locke wrote about pineapples in the context of philosophy because it was considered unique in taste and unobtainable to the common person due to cost, so it represented an idealized version of an idea that they could use in their work and would attract attention. My post on this topic pertains to pineapple within this timeframe, of which the year 1830 fits. It was at the time, coincidentally, that discussion about Fibonacci numbers and plants arose. My question is whether pineapples were discussed in this context at this time and used as an example, not whether it is of any importance to the math itself. Viriditas (talk) 02:17, 24 April 2024 (UTC)

The botanists credited with the discovery were Karl Friedrich Schimper and Alexander Braun. Schimper appears to have been the first (in 1830) to describe an observed phyllotactic pattern in term of the Fibonacci sequence (to wit, for the rotational angle between leaves in a stem) and his friend Braun described the next year a Fibonacci pattern in pine cones. I found no evidence these gentlemen or any other 19th-century scientists ever studied the patterns of pineapples. As reported here, the number of spiral rows of fruitlets in pineapples was studied "as early as 1933" by Linford, however, without referencing the Fibonacci sequence.  --Lambiam 16:45, 24 April 2024 (UTC)

Do you know where I can read their original work? I assume it is in German somewhere? It turns out that the history of the word "pineapple" has a lot of of confusion. "Pineapple" once referred to pine cones in English, while other languages used variations on "ananas" for pineapple, such as German. Viriditas (talk) 20:36, 24 April 2024 (UTC)

@Lambiam: I just found something interesting. This is unlikely to be true, but there is an implausible chance that Schimper & Braun were mistranslated: "Two names will exist side by side, and only after a time will one gain the upper hand of the other. Thus when the pineapple was introduced into England, it brought with it the name of 'ananas,' erroneously 'anana,' under which last form it is celebrated by Thomson in his Seasons. This name has been nearly or quite superseded by 'pineapple,' manifestly suggested by the likeness of the new fruit to the cone of the pine. It is not a very happy formation; for it is not likeness, but identity, which 'pineapple' suggests, and it gives some excuse to an error, which up to a very late day ran through all German-English and French-English dictionaries; I know not whether even now it has even disappeared. In all of these 'pineapple' is rendered though it signified not the anana, but this cone of the pine; and not very long ago, the Journal des Débats made some uncomplimentary observations on the voracity of the English, who could wind up a Lord Mayor's banquet with fir-cones for dessert." (On the Study of Words, Richard Chenevix Trench, 1893, p. 254.) Viriditas (talk) 20:51, 24 April 2024 (UTC)

Schimper 1830 and Braun 1831 are independently written articles. I have not looked at Schimper's article, but as described he only discusses the placement of leaves. Braun being an accomplished botanist, he would not have used the term Tannenzapfen (pine cone) as an ambiguous name for the fruit of Ananas comosus, and his article furthermore identifies specific species or at least genera of conifers (Weisstanne = Abies alba; Lerchen = Larix; Rothtanne = Picea abies) whose cones he studied.  --Lambiam 05:42, 25 April 2024 (UTC)

Thank you. This is even more confusing given that pine cones were also called pineapples. Viriditas (talk) 20:24, 26 April 2024 (UTC)

top of a pine cone

• I just uploaded this photo of the top of a pine cone. Can anyone get the Fibonacci numbers from it? I've seen drawings were they show the Fibonacci numbers, but they may be a little idealized, or maybe they had a better example. Bubba73 ^{You talkin' to me?} 06:36, 27 April 2024 (UTC)

The photo looks good to me. The two numbers in the sequence are 8 (spirals going right), 13 (spirals going left), from 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... Viriditas (talk) 07:12, 27 April 2024 (UTC)

It is really hard for me to count around the spirals. Bubba73 ^{You talkin' to me?} 23:55, 27 April 2024 (UTC)

I understand. What I do to help me focus is to open the image in full screen mode. Then, I place the index finger of my left hand on whatever spiral I designate as #1. Keeping my left finger on the screen on the location of the first spiral, I then take the index finger of my right, and use that as a pointer, so when I eventually end up back at the first position, I don't lose the count, which is how I get 8. Then I do it backwards, resulting in 13. My vision is very poor, so this is the only way I can keep track of the spirals. Viriditas (talk) 00:06, 28 April 2024 (UTC)

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