ELI5: Why can't we fully calculate Pi? What, if anything, would change if we could?
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Posted Mar 30, 2016, 2:34 PM UTC
06
Because it goes on forever. There are an infinite number of digits in pi so it is impossible to ever "fully calculate" it. We can calculate more and more numbers, but we can do this forever and there would still be an infinite number of more digits after whatever we've calculated.
1
Pi is an irrational number. It has no end so it can't be calculated exactly.
There is no real reason to calculate pi. All engineering projects can be more or less accurate from the first few digits of pi. Even ten or twenty digits are more than sufficient.
1
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1
Because it never ends. If we could change it, then circles wouldn't be circles. Pi is a measurement of a reality, so...for PI to be different, geometry would have to be different.
TL:DR; no more circles.
0
we haven't found an end to Pi and its unlikely to have a termination.
most computer systems are 64 bit at most, and are double precision, which means they can only have about 16 digits of accuracy. this is about as accurate as all engineering and scientific measurements and devices can be
0
We can fully calculate pi, pi = circumference / diameter, calculation finished.
We just can't express it with a finite number of decimal places, there are plenty of numbers like that.
What if pi could be expressed with a finite number of decimals places? Or essentially, what if it were rational?
Then math would be different. It is kind of like asking what if 2 + 2 = 5.
0
Pi is an irrational number. That is it cannot be expressed as a fraction, which is also called an rational expression. Further, an irrational number does not have a terminating or repeating expression after the decimal point. So for each digit after the decimal point there will always be another one.
3.14
3.141
3.1415
3.14159
3.141592
3.1415926
And so. There will always be another digit. And the pattern will not start over. So that is why we cannot ever get an exact number for Pi.
Having said, that if we could not a whole lot would be different. We only need about 39 digits of Pi to measure the circumference of the known universe accurate to the width of a single hydrogen atom.