1/22/2024 0 Comments Fibonacci sequence in seashells![]() Hearing "you're such a genius!" from everyone around him would not be good for his future self. I just hope he doesn't become a victim of his own success. this will always be a future de-facto "get-his-foot-in-the-door" for him, regardless of whatever it is he's trying to do. Obviously that assumes he plays his cards correctly going forward. Admissions boards, employers, investors, etc. That's going to impress virtually everyone he ever meets, probably. It demonstrates that even at age 13, he was a very capable real-world problem solver, while also showing off his ability to perform and present his own original research in ways that other people can build on. this link will forever be associated with his name. I'd even say Aidan's "set for life" that might seem over the top, but consider. On the other hand, whoever's taking care of him behind the scenes has done an incredible job. I wish Aidan had been allowed to write this in his own words, rather than his parent's / someone else's words. But again, you don't see those in the design books! (or sometimes you do but nobody bothers to check) very closely for small numbers).Ĭounting seeds in sunflowers shows that some of them follow the Lucas sequence instead of Fibonacci. However, the smaller ratios of those other sequences can be very different from the smaller ratios of the Fibonacci sequence (neither sequence approximates phi 0.618. there are many other number sequences of the same recurrence relationship as Fibonacci numbers that produce the same golden ratio. That is how you can tell that the organism "tries" to realize a close packing and just happens to produce the golden ratio and sometimes Fibonacci numbers as a byproduct: if the process would have been based on the golden ratio instead, a disturbance would cause a spiral out of control with many empty patches.įinally, I almost forgot his (and nearly implied otherwise in my previous post), just the fact that the golden ratio occurs in a process or system does not mean that Fibonacci numbers are involved. Sunflower seeds actually turn out to grow that way because the organism tries to pack the seeds as close as possible.įrom this, if the close-packing manages to occur without disturbance, the golden ratio emerges-but if it is disturbed by anything (disease, damage, etc), the golden ratio becomes less accurate but the organism still continues packing the seeds as closely as possible. Oh some more things, re-reading that lovely "Fibonacci Flim Flam" essay I linked above, it turns out that: Because really it's super easy for fibonacci numbers to pop up anywhere, especially the small ones, what's significant, however, is when the golden ratio actually plays a meaningful role. I kind of wonder, though, if it's not the other way around-because nature uses golden ratio angles in tree branches, the fibonacci numbers pop up. So I can imagine if you apply this to the rotation of tree branches, it'll result in a more uniformly distributed pattern, that will capture sunlight more efficiently than a pattern with holes in it. The thing about this particular pattern is that the seeds end up being rather uniformly spaced over the plane, while using other angular ratios creates swirly patterns and waves of filled and empty regions. If you divide the 360 degrees of a circle in two parts so that their ratio is 1:1.618, and you use that angle (about 137.5 degrees) to rotate outwards as a spiral, put a big dot at every point, you'll get a pattern that looks pretty much exactly like sunflower seeds. ![]() The one thing where he is right, is the pattern in sunflower seeds. It's imprecise enough that you really can't say whether people like 1.5 (3/2) or 1.667 (5/3) or 1.618 (phi) best. ![]() Nor is there anything "inherently beautiful" about the golden ratio, research into perceived aesthetics of ratios simply showed that people prefer fractions of small numbers. It's a very tasty popular myth that people like to repeat, that there's a magical sacred golden constant producing all the complexity in nature and more.Įxcept that nobody actually bothers to measure anything, they just keep repeating and reposting the same images of spiral galaxies and nautilus shells. What's more mysterious is that the "divine" number equals your height divided by the height of your torso, and even weirder, the ratio of female bees to male bees in a typical hive! (Livio)Įxcept that most of this is simply not true: Scientists and naturalists have discovered the Fibonacci sequence appearing in many forms in nature, such as the shape of nautilus shells, the seeds of sunflowers, falcon flight patterns and galaxies flying through space.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |