So I know that pi is the ratio of a circle’s circumference to its diameter (and the ratio of r³x4/3 to the volume of a sphere).
Apparently even the circumference of the universe needs less than 40 decimal places to be more accurate than we would ever need to worry about.
So my question is, how do we determine the decimal points beyond this? If pi is a ratio and even the largest conceived circle only gets you to ±36 places, how do we determine what the subsequent numbers are?
One thing to be aware of is that if you actually made a circle and measured its radius and circumference you wouldn’t get pi. Not because your measurements would be off, but because the universe does not follow the assumptions mathematicians used to define pi—namely Euclidean geometry. Pi is mathematical, not physical. If real circles and real diameters don’t give you pi that is a problem for the universe, not a problem for mathematics.
Wat?
The universe is non-Euclidean, so no circle made in the actual geometry of the universe actually has the ratio of pi between its circumference and diameter.
Is that the part you are confused about, or did I write something else badly?
[finding people who don’t know that we live in non Euclidean space these days is like finding people who think the sun goes round the earth. But I guess if people can’t be bothered to learn 350 year old mathematics, they also can’t be bothered to learn 100 year old physics. Oh well.]
The universe being non euclidian needs some extraordinary evidence.
It’s true! I just drew a circle and measured it. Turns out π≈5.
How do people calculate pi
They don’t.
Pi is well known, up to many more than hundred digits. People memorize it, or look it up, but they don’t need to calculate again (unless they want to go to extremes).
Right, but, somebody had to calculate what those digits were before we knew them.
Pi is well known, up to many more than hundred digits.
They’re asking how this is known…
