Base 12 being 3-smooth, any number with 2 or 3 as a factor has a reciprocal with a terminating expansion.
base 60 is 5-smooth, so any number with 2,3,5 as a factor has a terminating expansion.
Just as SI has to add in deg min sec for fields like astronomy.
As the practical numbers are quite dense up to 60, they could divide by multiplication of the reciprocal for many more numbers.
Floating point is more complicated than just the base as the radix also matters. C(++) finally got decimal radix support this year in the standards and IBM has had decimal floats for a long time.
FFT and encryption often use mixed radix despite being a binary base too.
It is a far more complicated subject than it appears on the surface.
But there are problems that aren't easily solvable in base 10. The degrees of a circle are an example and why navigation uses the nautical mile, where 1 nautical mile= 1 minute of latitude is an example.
12,60,360 are Superior highly composite numbers and 12 is the smallest 3-smooth and 60 is the smallest 5-smooth.
This also means that with using 360 degrees one can divide a circle or semicircle in 12 sections with just a square, 345 triangle and equalatrral triangle. Where decimal or even radians requires the square root of 2, pi, etc...
I am a fan of universal units of measurement, but had they been base 12 it would have been better IMHO. SI could be more broadly adopted if it has been base 12.
Seximal is actually great for hand counting. You can use fingers the classical way for one digit per hand or base 6² compression for two digits per hand, allowing you to count up to 1296 with two hands.
base 60 is 5-smooth, so any number with 2,3,5 as a factor has a terminating expansion.
Just as SI has to add in deg min sec for fields like astronomy.
As the practical numbers are quite dense up to 60, they could divide by multiplication of the reciprocal for many more numbers.
Floating point is more complicated than just the base as the radix also matters. C(++) finally got decimal radix support this year in the standards and IBM has had decimal floats for a long time.
FFT and encryption often use mixed radix despite being a binary base too.
It is a far more complicated subject than it appears on the surface.
But there are problems that aren't easily solvable in base 10. The degrees of a circle are an example and why navigation uses the nautical mile, where 1 nautical mile= 1 minute of latitude is an example.
12,60,360 are Superior highly composite numbers and 12 is the smallest 3-smooth and 60 is the smallest 5-smooth.
This also means that with using 360 degrees one can divide a circle or semicircle in 12 sections with just a square, 345 triangle and equalatrral triangle. Where decimal or even radians requires the square root of 2, pi, etc...
I am a fan of universal units of measurement, but had they been base 12 it would have been better IMHO. SI could be more broadly adopted if it has been base 12.