Fibonacci sequence

Speleotron

Speleotron

Member
And presumably he thinks that the harmonic scale developed in Western culture has some kind of fundamental significance? I think that kind of thing can be fun as long as people realise that it has no underlying meaning or mathematical significance.

By the way I'm not sure that the digits of pi really are random. They don't repeat, that has been proved, but asking whether they are random leads down a rabbit hole. I would say that the digits of pi are not random as there is a formula for finding the nth digit of pi, allbeit in hexadecimal, but nature doesn't favour base 10.

https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
https://stats.stackexchange.com/questions/44445/are-the-digits-of-pi-statistically-random
https://www.jstor.org/stable/2685604?seq=1#metadata_info_tab_contents
https://www2.lbl.gov/Science-Articles/Archive/pi-random.html
 
Brains

Brains

Well-known member
mikem said:
Is Pi the same if you work in hexadecimal then?
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Being a ratio, the proportions will be constant, regardless of the units used or the base of the numbers... The actual numerical values are relevant?
 
Speleotron

Speleotron

Member
Any number is the same in any base it just doesn't look the same. The base is just how we display it on a page, nature doesn't care. We probably use base 10 because we have 10 fingers and the Romans didn't use any base as their numerals don't work like that.
 
Speleotron

Speleotron

Member
I'm not sure, I was making an educated guess, but with 10 fingers you tend to count in tens, so you might imagine our ancestors counting in convenient blocks of 10, e.g. '4 tens and another 3 fingers' or '10 tens of tens, and another ten, and 4 fingers' which is essentially base 10. This goes into some detail:

https://math.stackexchange.com/questions/8734/why-have-we-chosen-our-number-system-to-be-decimal-base-10

"

    Traces of the anthropomorphic origin of counting systems can be found in many languages. In the Ali language (Central Africa), for example, "five" and "ten" are respectively moro and mbouna: moro is actually the word for "hand" and mbouna is a contraction of moro ("five") and bouna, meaning "two" (thus "ten"="two hands").

    It is therefore very probable that the Indo-European, Semitic and Mongolian words for the first ten numbers derive from expressions related to finger-counting. But this is an unverifiable hypothesis, since the original meanings of the names of the numbers have been lost."
 
C

Canary

Member
Numberphile did a bit on it:

https://www.youtube.com/watch?v=sj8Sg8qnjOg

Not sure where the original claim came from though, might have slowly morphed from sunflowers?
 
ChrisJC

ChrisJC

Well-known member
You can of course have a number system where Pi is used as the base.

I think there are drawbacks to this though.

Chris.
 
Speleotron

Speleotron

Member
That's interesting, in my head I always count things in 20s. I just remember the number of 20s, and then the number of units less than 20 left over. I've always found 20 to be a practical size.
 
F

Fjell

Well-known member
I read this as a teenager shortly after it came out and it cured me of ever worrying about this sort of thing ever again:

https://en.wikipedia.org/wiki/G?del,_Escher,_Bach

Going caving just seemed easier.
 
M

mikem

Well-known member
6 is the number they reckon you can keep track of without having to count.

& 12 (60 / 360) for times & angles as they divide by more numbers - 1;2;3;4;6 etc
 
Speleotron

Speleotron

Member
The Babylonians were ahead of their time in realising the importance of using numbers that have lots of factors. I wonder if it gave their economy an edge?

I remember reading that, in ancient egypt 4000 years ago, to enter the civil service you had to pass a maths test. People used to sell books to help people pass the test, the blurb on one of them said something along the lines of 'if you are a farmer you will work yourself to death, if you are a fisherman you will drown, only the scribe is happy. This book will teach you the secrets and allow you to pass the test.' I'll have to see if I can find the book online. I find it amazing that this went on 4000 years ago, it reminds me of 'coding bootcamps' these days which promise to take people from minimum wage to a six figure tech salary.
 
F

Fjell

Well-known member
Speleotron said:
It's strange how many people say 'worrying' in this context, number theory isn't a source of anxiety it's fun!
Click to expand...

It certainly cured me of applying to do maths at uni. I realised I was more into building things and doing stuff, even if I could do the maths.
 
Mrs Trellis

Mrs Trellis

Well-known member
As you may be aware I'm a fan of BBC Radio 4 factual programmes  :read:  so here is the "In our Time" programme on the Fibonacci sequence:-

https://www.bbc.co.uk/programmes/b008ct2j
 
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