> But π=3.14159265358979 is a time bomb! Sooner or later it will fail you when it’s not accurate enough anymore.
If you know the exact diameter of the sun, and calculate the circumference with 3.14159265358979 as an estimate for pi, then your error will be about 10 microns. Using a 14 digit estimate of pi, is never going to be a timebomb for any practical task. If the earth was round to 14 significant digits the highest mountains would tower 10 nanometers above the deepest valley.
But the sun isn't a perfect sphere. If you're using pi to calculate the circumference of the sun, and need any sort of accuracy, you're doing it wrong - you're answering a question with no relation to reality.
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> But π=3.14159265358979 is a time bomb! Sooner or later it will fail you when it’s not accurate enough anymore.
If you know the exact diameter of the sun, and calculate the circumference with 3.14159265358979 as an estimate for pi, then your error will be about 10 microns. Using a 14 digit estimate of pi, is never going to be a timebomb for any practical task. If the earth was round to 14 significant digits the highest mountains would tower 10 nanometers above the deepest valley.
You are saying, I think, that we won’t ever need to know π beyond some accuracy. By saying that you, if you are right, are doing good math.
But the sun isn't a perfect sphere. If you're using pi to calculate the circumference of the sun, and need any sort of accuracy, you're doing it wrong - you're answering a question with no relation to reality.