Posted on 04/21/2017 9:41:09 PM PDT by MtnClimber
For hundreds of years until the ebb of the Italian Renaissance, one name was synonymous with arithmetic. This was Leonardo — not the polymath from Vinci, but Leonardo Pisano (ca. 1170-1250), now popularly known as Fibonacci.
Yet we know little of Fibonacci’s life beyond the nickname and his Pisan roots: most details come from a 160-word autobiographical sketch written in 1202. He is often assumed to have discovered the so-called ‘Fibonacci sequence’, which starts with zero and 1 and is thereafter the sum of the two previous numbers (so 1, 2, 3, 5 and so on). The sequence shows up with astonishing frequency in natural spiral structures such as shells and plant tendrils.
Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC. Nor does the sequence explain anything about artistic beauty via the so-called ‘golden section’, as Keith Devlin reminds us in his new book Finding Fibonacci. The Pisan’s greatest legacy was to help Europe dump the ancient system of Roman numerals and switch to Hindu-Arabic numbers from 1 to 9 and, perhaps most importantly, 0, which Fibonacci called zephirum after the Arabic ṣifr.........
Roman numerals made multiplication and division extremely cumbersome (try dividing MXCI by LIII); they were no match for the 10-digit positional system invented by the Hindus some time before 700 AD and common in the Arab world. And compared to using, say, an abacus, calculations in Hindu-Arabic numbers also allowed an “audit trail”, as Devlin points out: “An individual sitting in Pisa controlling a network of traders needed to be able to review the financial books on a regular basis.”
(Excerpt) Read more at blogs.nature.com ...
When our oldest was in first grade he was selected for a science pull out class. He came from the first session disgusted, “She didn’t even know what a Fibonacci number is!” The teacher told us the same story, amazed that he was looking for the Fibonacci pattern on the sea shell.
Thank you Jonathan Park cds! Kids learned a great deal while being entertained.
I recently “rediscovered” the calculations of Al-Khashi, from the 1400’s by using the same method, an approximation of pi by the circumference of a polygon. I found that this devolved onto the half-angle formula for sine, or equivalently for cosine, applied recursively. This is a trigonometric formula, but easily obtained by direct geometric construction.
I did all this on my own and I was amazed to see how closely I had followed Al-Kashi’s method. Of course it was very easy for me to carry the recursions much further, using the UNIX based extended precision calculator, bc .
Al-Kashi obtained 17 decimal digits of pi, and it is quite amazing to me how modern his thinking was concerning this recursive computation.
Yes, amazing that that precision was achieved so long ago.
Beaumarchais(Marriage of Figaro, Barber of Seville) put his life saving in the cataloging and publishing of Voltaire's manuscripts and documents. Voltaire gave his blessing.
When finished(after the death of Voltaire), Beaumarchais was ask to summarize the thousands of documents in a few words. I think you know what he said...."I disapprove of what you say, but I will defend to the death your right to say it"
Most of my math these days is converting GEO satellite orbits with inclined orbits from polar coordinates and predicted drift to cartesian coordinates for satellite terminal tracking changes. That and link budget data rate calculations.
bmfl
I have read that the ancient Greeks calculated the cicumference of the earth nearly 2500 years ago. When compared to what we know now about the earth’s actual cicumference they were only off by a couple hundred miles.
CC
What we realize now as math and physics were important too - to God I think - in creating the universe.
When I was in college at University of Florida, College of Electrical Engineering I spent time trying to understand Einsteins Theory of General Relativity, but got lost at the Taylor Series Expansions.
At the time I thought that Maxwells Equations and the derivations were obvious and I thought I could have derived them if Maxwell had not. Now I have forgotten much of that and know satellite dynamics these days.
My first engineering boss and VP of engineering was a member of some Fibonacci society and had a stack of their quarterlies around. I was overwhelmed by work all day and school at night, so never had the spare brain cells to bother looking into the magazines.
Would like to see a few of those now, though probably very dense reading.
Can’t follow you here! The Taylor series is an elementary and familiar tool. I can only suppose that you are referring to material covered by THE LINEARIZED THEORY OF GRAVITY in the MTW “phone book”. I wouldn’t think this would be a hurdle except that in a course on the subject, this would be the basis for a lot of calculation.
Well, I’ve got no business speaking up at all, since my understanding of the subject is largely illusory!
Cheers.
Now you are on very daring ground! I would imagine that in the Middle Ages you may have doomed yourself with such talk, insofar as you are intimating, though not stating, restrictions on God’s creation.
But, you did tread lightly! I think you might have got off with any kind of leniency.
To be specific, I think it’s hard to avoid the idea that logic and math are coexistent with God, and not subject to His Creation. Well then, what of Physics? What of the Universe? I think we are left without any sort of account, except that “God Said”. Please don’t think that I am mocking! Here I am.
Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC. Nor does the sequence explain anything about artistic beauty via the so-called ‘golden section’, as Keith Devlin reminds us in his new book Finding Fibonacci>>>>>>>>>>>
The Golden Mean allegedly debunked by an Arabic touch stone?
Fibonacci sequence describes far to many shapes in nature. NO DEBUNK!
The Great Pyramid also calculates the Earth’s circumference and is only off by feet - done almost 3000 years before the Greeks.
The Golden Mean was the primary design tool of Ancient Egypt 3000 years prior.
The Golden Mean was the primary design tool of Ancient Egypt 3000 years prior.>>>>>>>>>>>>>>>>>>>>>
Yes, I know, that’s why I consider this thread article to be exceedingly shallow and ahistorical.
The Golden mean describes the fundamental nature of our three dimensional realm and its relationship to various forms of energy, a bridge between the material world ,and the world of energy.In the opld sense or saying, “ joining heaven and earth”
Knock
Knock Knock
Knock Knock Knock
Who's there?
Fibonacci
So the journalist gets the fibonacci sequence wrong... Is it any wonder math is dead...
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