1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
Obviously not an emergent property but shows how these things were designed.
1m = 1e-10 times half-meridian from the North Pole to the equator, via Paris for a croissant, apparently.
So kind of a coincindence... But a very neat one. Meanwhile, ratio of adjacent Fibonacci numbers converves to some expression involving sqrt(5) which is approx 1.6
https://en.m.wikipedia.org/wiki/History_of_the_metre
https://en.m.wikipedia.org/wiki/Arc_measurement_of_Delambre_...
5! 120 however lacks fine precision required at human scale. Haven't done the math but it's probably something like using 3.1 as the analog of Pi.
360 seems like it might have been chosen based on a mix of precision and practicality. Many small prime factors ( 2 2 2 3 3 5 ). Also an extra prior prime factor for every added prime. 75600 too big, and 12 what analog clock faces use as their primary number.
Like minutes and seconds.
The 12 hours in a day and the 12 months are also 60 / 5.
This all connects to ancient Mesopotamia somehow.
I guess, for a sufficiently large value of 12.
Not that these are exclusive, but I thought it's a rounding of 365.25 days a year stemming from Egypt. 360 is a pretty useful number of degrees for a starry sky that changes ince a night.
60: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
100: 2, 4, 5, 10, 20, 25, 50
360: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
¹ https://mathworld.wolfram.com/SuperiorHighlyCompositeNumber....
By this logic, 0.016 (recurring) seconds should be a called a "third".
"minute" comes from latin "pars minuta" and the "i" should be pronounced like in "minimum"
> By this logic, 0.016 (recurring) seconds should be a called a "third".
It should be "tertia". I found that in German and Polish it was used that way, but don't know about english:
Commodores had a 1/60 second "jiffy" for timing interrupts, that's all I could find.
Later societies inherited that from them along with 60 minutes in and hour.
"The standard among mathematicians for writing larger bases is to extend the Arabic numerals using the Latin alphabet, so ten is written with the letter A and eleven is written with the letter B. But actually doing it that way makes ten and eleven look like they're too separate from the rest of the digits so you can use an inverted two for ten and an inverted three for eleven. But those don't display in most fonts so you can approximate them with the letters T and E which also happen to be the first letters of the English words ten and eleven. But actually as long as we're okay for using the Latin alphabet characters for these digits then we might as well use X for ten like in Roman numerals. But actually now we're back to having them look too different from the other ten digits so how about instead we use the Greek letters Chi and Epsilon but actually if we're using Greek letters then there's no association between the X looking letter and the number ten, so maybe you can write ten with the Greek letter delta instead.
And all you really need to learn is those 'two new digits' and you're ready to use dozenal."
- Jan Misali in his comedy video on why base 6 is a better way to count than base 12 or base 10 https://www.youtube.com/watch?v=qID2B4MK7Y0 (which is a pisstake and ends up making the point that Base 10 isn't so bad).
("in dozenal, a seventh is written as 0.186X35 recurring because it's equal to one gross eight dozen ten great gross ten gross three dozen five eleven gross eleven dozen eleven great gross eleven dozen eleventh's").
Now do PI!
Then Tom Lehrer's New Math.