> Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC.
Possibly even earlier. This is not developed further because the article is about Leonardo.
Pingala's is perhaps the first recorded conception of the sequence. It showed up in his study of metre and rhythm of poetry. The problem he was trying to solve was to enumerate how many ways can an integral period of time be broken up into pieces of unit and double unit length.
If you are a drummer I think this will make a lot of sense.
Pingala is also known for his use of binary numbers, 'Pascal's' triangle, recursive generation of strings from context free grammars. Full formalization of Sanskrit grammar as a context free grammar goes to Panini (possibly his brother).
I'm always surprised by the abstraction level of Sanskrit ideas. Very rapidly they talk about infinite ways of assembling rules. Was there even a strong motivation (economic or logistical value) behind this?
“Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués.
By the time Fell found a new publisher, Springer Verlag (now part of the same publisher as Nature), floppy disks had been superseded and she had to hire a hacker to extract the files. Fell then discovered that Springer only accepted submissions in TEX format, the technical standard for physics and mathematics texts. She learned it and spent six months retyping the text. Fibonacci’s Liber Abaci was finally published in 2002 — the 800th anniversary of the book’s first appearance.”
> Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC.
Possibly even earlier. This is not developed further because the article is about Leonardo.
Pingala's is perhaps the first recorded conception of the sequence. It showed up in his study of metre and rhythm of poetry. The problem he was trying to solve was to enumerate how many ways can an integral period of time be broken up into pieces of unit and double unit length.
https://en.wikipedia.org/wiki/Fibonacci_sequence#History
If you are a drummer I think this will make a lot of sense.
Pingala is also known for his use of binary numbers, 'Pascal's' triangle, recursive generation of strings from context free grammars. Full formalization of Sanskrit grammar as a context free grammar goes to Panini (possibly his brother).
https://en.wikipedia.org/wiki/Pingala
I'm always surprised by the abstraction level of Sanskrit ideas. Very rapidly they talk about infinite ways of assembling rules. Was there even a strong motivation (economic or logistical value) behind this?
I don't know enough to know why, but they were very interested in the extremes of size, both large and small, as well as the notion of infinite.
Fascination with the large seems to be a pan-cultural thing
https://en.wikipedia.org/wiki/History_of_large_numbers
The article does not talk about Mayan numbers, I would hazard a guess that they were interested in large numbers too.
There is also the Buddhist myth of Buddha enumerating a list of very large numbers.
https://en.wikipedia.org/wiki/Asa%E1%B9%83khyeya
https://jain108academy.com/buddha-recites-to-infinity-a-love...
Large numbers also show up in that problem posed by Archimedes.
https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem
https://sites.google.com/site/largenumbers/home/2-3/p12_2-3-...
Quoting:
“Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués.
By the time Fell found a new publisher, Springer Verlag (now part of the same publisher as Nature), floppy disks had been superseded and she had to hire a hacker to extract the files. Fell then discovered that Springer only accepted submissions in TEX format, the technical standard for physics and mathematics texts. She learned it and spent six months retyping the text. Fibonacci’s Liber Abaci was finally published in 2002 — the 800th anniversary of the book’s first appearance.”
I admire the devotion of her to her husband and to the work of his