this post was submitted on 01 Oct 2023
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Today I Learned
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So, pi involves measuring circles. In fact, just think of a pie. It's a circle, right? There you go. The observable universe is the size of forty of those circles (or pies, shortened to "pi"). The size of it all just blows your mind. As for the hydrogen atom, single atoms are tiny, so you can safely ignore it.
We're closer in scale to the observable universe than a single hydrogen atom if that's any help.
You get it.
No... Pi is a unitless number representing half a circles angular size.
Forty in the title is the number of digits, the title means that the relative size of the universe compared to a hydrogen atom is 1 followed by 40 zeros. Pi needs to be known to that accuracy to have a proper amount of significant figures.
Imagine trying to measure an ant with an unmarked foot long ruler. Not going to work super well. Your measurement uncertainty is +/- 6 in or 0.5ft. Well above the size of any ant.
Adding in inch marks improves that to +/- 0.5 in or +/- 0.042 ft. Closer to some ants, maybe about right, still not going to give you a measure of the ant but you'll be able to say if it's more or less than that. Now measure a circle with this ruler, to get the full accuracy of the ruler, you need only know pi to 4 digits., 3.142. Roughly. Actual uncertainty has some additional stuff going on, but without getting into it there you go.
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