18 May 14
1 edit
Originally posted by JS357Yes, so both of us know the exact value of pi in base pi.
It can be expressed exactly in base pi, in which case it is 10. Right?
In any base, the base is expressible as 10. I think.🙄
For another interesting irrational base see:
http://en.wikipedia.org/wiki/Golden_ratio_base#Representing_irrational_numbers_of_note_as_golden_ratio_base_numbers
18 May 14
Originally posted by twhiteheadNo - not an exact number of digits, but an exact value of pi.
And that is the problem. There is no such thing as using exactly an infinite number of digits.
Its like saying 'you could count to infinity if you counted all the integers'. Its incoherent because there is not actual number called 'infinity'.
18 May 14
Originally posted by twhiteheadWell there is one hitch in all that: IF we live in a multiverse there may be versions of our universe with slightly different laws of physics, like the difference between mass of proton Vs electron or some such or the gravitational constant. If G changes circles might change since you do circles in space time. If spacetime is somehow different there PI COULD change a bit.
No, universal truths, are by definition, universally true. You might argue that the value of pi is not a universal truth, but you cannot claim that universal truths are changeable.
And the value of pi possibly depends on certain axioms but not on cosmic circumstances, so it is not changeable in extreme cosmic circumstances.
If the axioms are false, then ...[text shortened]... t rather solely on definitions. So it may not even be a 'truth' at all, but rather a definition.
Besides, this being could play with the digits 10 trillion away from the first 9 or so and have not one whit of difference in practical outcomes.
18 May 14
Originally posted by sonhouseAs already pointed out, we do not do circles in spacetime. We do them in Euclidian geometry. It is already the case that circles in spacetime do not have a circumference of 2*pi*r^2 as spacetime is not flat. Similarly, triangles in space time do not have angles that add up to 180 degrees.
If G changes circles might change since you do circles in space time.
If spacetime is somehow different there PI COULD change a bit.
Pi is a mathematical constant, not a physical constant. As already pointed out, it is obtainable from certain sequences. Those sequences have nothing whatsoever to do with the specific spacetime we live in.
Besides, this being could play with the digits 10 trillion away from the first 9 or so and have not one whit of difference in practical outcomes.
The discrepancy between circles in space time and Euclidean circles is quite a bit more significant than that - depending of course where you measure. Near a black hole it gets really significant.
18 May 14
1 edit
Originally posted by JS357But isn't that derivation of pi obtained through Fourier series expansion which of course involves sines and cosines, the values of which dependent of the basic geometry of circles!?
Related question: does an omniscient being know the exact numeric value of pi? (Say, in base 10.)
BTW, most people think of pi in its geometric sense but it is also the numeric value of a mathematical series expansion. More than one series expansion, actually.
Here's one: PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ...
or PI = 4(1/1 - 1/3 + 1/5 - 1/7 + ...)
alternating + and - and using odd integers.
http://math2.org/math/constants/pi.htm
(Been too damned long since I actually did any of that stuff - oh how I miss the good old days of uni 🙁 )
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18 May 14
Originally posted by AgergWell the problem I see is that you have to use the exact values of irrationals like 1/3 and 1/7 to calculate it. Maybe that says the same thing.
But isn't that derivation of pi obtained through Fourier series expansion which of course involves sines and cosines, the values of which dependent of the basic geometry of circles!?
(Been too damned long since I actually did any of that stuff - oh how I miss the good old days of uni 🙁 )