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Mathematically speaking, Pi can’t be “simplified”, but I’m personally curious what ratio is Pi to the highest precision necessary to calculate anything tangible
by inlined 7y ago
Mathematically speaking, Pi can’t be “simplified”, but I’m personally curious what ratio is Pi to the highest precision necessary to calculate anything tangible (the circumference of the universe to the Plank length). Practically speaking one could say that is the simplification of Pi.
- saagarjha 7y agoYou'd need something along the lines of 60ish digits: https://www.wolframalpha.com/input/?i=diameter+of+the+observable+universe%2Fplank+length https://www.wolframalpha.com/input/?i=diameter+of+the+observ...
- rrauenza 7y agohttps://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/ https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimal... Let's go to the largest size there is: the visible universe. The radius of the universe is about 46 billion light years. Now let me ask a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom (the simplest atom)? The answer is that you would need 39 or 40 decimal places. If you think about how fantastically vast the universe is — truly far beyond what we can conceive, and certainly far, far, far beyond what you can see with your eyes even on the darkest, most beautiful, star-filled night — and think about how incredibly tiny a single atom is, you can see that we would not need to use many digits of pi to cover the entire range.