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@caesar-salad saidMust have been useful...golden ratio used lots in Art
I somehow landed on that about 40 years ago when I was a young painter (at the time, I also tried mapping the optical-complement color wheel against the 12-tone musical scale -- I think Newton did something similar, much earlier).
How sad that a poster has seen for to pollute this thread with a veiled criticism that the number sequence is accorded 'Fibonacci'
Who can say who very first discovered/looked at this arrangement of numbers?
@blood-on-the-tracks saidLet's not be too hard on any fellow sprout among us, for we all have to navigate a composite wilderness, wittingly or not, and not just involving the Fibonacci Series but perhaps also some Lyapunov and Mandelbulb influences, and strange attractors as well.
Must have been useful...golden ratio used lots in Art
How sad that a poster has seen for to pollute this thread with a veiled criticism that the number sequence is accorded 'Fibonacci'
Who can say who very first discovered/looked at this arrangement of numbers?
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@Duchess64
Also traced back to Pingala, an Indian mathematician, from over 2000 years ago.
You seem to have hijacked this thread, which developed into a reasonably interesting discussion on the links between Fibonacci/golden ratio/ Mile to km conversion, into one on which you are googling theorems and telling us that the person they are named after did not first discover them.
Mostly, of course, Western mathematicians (or, at least, their 'followers'. ) being cited for plagiarizing non Western mathematicians work. (Well, ALL, actually)
And thumbing myself and other posters 'down' , which is just childish.
Good job
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@Duchess64
Yep. I alerted it as being totally 'off topic' Don't think anyone can argue against that.
I see you alerted my post replying to your witterings about Pascal.
We'll see how that works out - I guess it could also be argued as being 'off topic', so fair enough of it goes (although I did mention the word 'Fibonacci'! )
As could this one. Almost a Fibonaccian accumulation of off topic posts from one original one.
@Duchess64
Why do you want to divert talk about Fibonacci numbers into a political scree? What difference does it make who discovered it first? Newton invented calculus but so did Leibniz but do you think it now is a political argument against Newton? Why can't you post work done lately by mathematicians rather than going into political debates about who invented what?
My guess is any modern mathematician worth their salt would already know about ancient works.
@sonhouse saidNewton "kind of" invented calculus, but it was really many different mathematicians spanning a couple centuries who contributed to its construction. Only Cauchy and Weierstrass, I think, finally put some rigor into it with the epsilon-delta definition of limit and other niceties -- a century or more after Newton's demise.
@Duchess64
Why do you want to divert talk about Fibonacci numbers into a political scree? What difference does it make who discovered it first? Newton invented calculus but so did Leibniz but do you think it now is a political argument against Newton? Why can't you post work done lately by mathematicians rather than going into political debates about who invented what?
My guess is any modern mathematician worth their salt would already know about ancient works.
https://en.wikipedia.org/wiki/Augustin-Louis_Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (/koʊˈʃiː/;[1] French: [oɡystɛ̃ lwi koʃi]; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra.
The calculus of Newton and Leibniz was replete with "fluxions," "infinitesimals," and other nonrigorous twaddle that could not be employed to convincingly prove most of the core theorems of calculus.
@sonhouse said"History of mathematics" courses, I'm sorry to say, are rarely taken by mathematics majors. And I am sorry to say it, because maybe it should be required. Usually such courses are taken by aspiring K-12 teachers, and perhaps philosophy majors.
My guess is any modern mathematician worth their salt would already know about ancient works.
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@Soothfast
You too are going off piste!
To bring us back to good old Fibbo, can anyone give me a formula for the nth term in Soothfasts Fibbo sequence (LHS)?