Meme of two women fighting while a man smokes from a pipe in the background.
The women fighting are labeled "mathematicians defining pi" and "engineers just using 3 because it's within tolerance"
The man smoking is labeled "astrophysicists" and the pipe is labeled "pi = 1"
38 digits of pie gives youv an error of less then a hydrogen atom in the circumference of the known universe.
https://www.jpl.nasa.gov/edu/news/how-many-decimals-of-pi-do-we-really-need/
Using 1 is fun. That means the circumference of a circle is equal to its diameter.
Isn't this functionally true for objects on the infinite focal plane? I.e. a star? Betelgeuse might actually be huge in absolute terms, but from earth, and even in a large telescope, it's still a pinpoint whose circumference is not meaningfully distinct from its diameter.
It would be the size of the telescope's diffraction artifacts probably. Meaning the shape you see on the picture is not related to the size of the star but only to the physical limits of the optical instrument. This diffraction pattern is proportional to the color your looking at and inversely proportional to the size of the telescope primary mirror. The bigger the telescope primary mirror, the smaller the diffraction pattern and the more chance you have that this artifact will not completely hide the object you are looking at. I didn't do the math, but I guess to image the actual disk of Betelgeuse, the size of the telescope you need is probably still science fiction, even with interferometry.
I want you to know that you nerd sniped me with this comment and I started doing the math. To raise the apparent size of Betelgeuse to the apparent size of Jupiter (at its largest to the naked eye), you'd need a minimum 20 inch aperture telescope to pull the required 1000x magnification. Mind you:
20 inches is not a mass produced telescope size, but there ARE custom makers who produce reflectors at and well beyond this size. There are certainly terrestrial telescopes that can achieve what we need.
you're still not resolving any details at that size, it's just raising Betelgeuse to the same apparent size as Jupiter at its naked eye largest.
most places on earth are not conducive to magnifications over 300x. You can certainly do it, and sometimes the atmospheric conditions are ridiculously clear and you can pull off stupid levels of magnification, but there's a reason why observatories get built up on mountains a lot. 1000x is... Well, good luck. Especially since Orion and Betelgeuse never get too close to the zenith, meaning there's always a substantial amount of atmosphere to deal with.
Edit: let's go with raising it to the same apparent size as the full moon, which occupies about 30 arcminutes or 1800 arc seconds. Jupiter is 50 arc seconds at the largest, and Betelgeuse is 0.05 arc s. To figure out how much we need to magnify Betelgeuse by, we take the apparent size of the moon and divide it by the apparent size of Betelgeuse, yielding 36,000x. Assuming a spherical cow, telescope aperture is what limits the maximum useful magnification, and the equation to derive that is roughly 50x aperture. So, if we divide 36,000 by 50, we'll get our minimum required aperture of 720 inches, or fifty feet. IIRC, we have at least one terrestrial telescope that's at least that large, down in Chile, though I'm almost certain there are more and larger ones, too.
Euclidean geometry enjoyers in shambles
As a retired mechanical engineer, the joke is that we don't really remember the value of Pi, but we think it's somewhere around 3. But maybe we should use 4 just to be safe.
In any case, I have to remember 3.14 because one of my Daughters was born on Pi Day. Which, according her, is the second most important day of the year, just right behind Christmas Day, when she was growing up. So when she got into high school that meant that we had to bring enough pie to be served in each of her math classes on that day. (Oddly enough she prefers cheese cake over pie on her Birthday).
Now I'm not saying being born on Pi Day influenced her life any, but she has a PhD in Mech Engineering.
Good news for her. Cheese cake is a pie not a cake.
This made my day.
Solidifies my preference for pie over cake
You sound like an involved and caring father. Rock on, dude
Theres a YouTube video where the presenter demonstrates DOOM running (or not) with varying values of Pi that's quite interesting: Non Euclidean DOOM
Electrical engineer. Never used 3. Always 3.14. don't really get the joke.
I've seen some blueprints who use 3.5. I guess it's close enough but definitely not too small
38 digits of pi can get the circumference of the visible universe to within a single hydrogen atom.
10 digits gets the diameter of the earth to within an inch.
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10 digits gets the diameter of the earth to within an inch.
Put another way, 10 digits means that your error will be caused by your imprecise model of the Earth's shape, rather than imprecision in the value of pi.
And just two digits introduces less error than your average terrible model
Wow, what do you have against models? I mean, I know that the trope is that they aren't very smart, but the same trope applies to firemen, so why pick on models?
old man voice this must be that ragebait thing the youngsters are always talking about
The real comment mvp. You deserve every positive vote my post got
out of curiosity... does that first fact account for the continued expansion of the universe?
It works at the current 93 billion light years of observable universe (46ish in every direction)
Computer science: pi is O(1)
Is it actually? I'll admit im pretty rusty on time complexity, but naively I'd think that pi being irrational would technically make even reading or writing it from memory an undecidable problem
If you're trying to calculate it, then it's quite difficult.
If you just want to use it in a computer program, most programming languages have it as a constant you can request. You get to pick whether you want single or double precision, but both are atomic (a single instruction) on modern computers.
Do said atomic instructions produce pi though, or some functional approximation of pi? I absolutely buy that approximate pi is O(1), but it still seems like a problem involving a true irrational number should be undecidable on any real turing machine
The "true value of pi" is too large for any computer to store. Our current understanding of numbers says it's an infinite number of digits. On the other hand, any number you use to multiply with pi is far less than an infinite number of digits. So you get the correct answer, with no worse precision than your input value, using the approximations of pi.
What would be the "n" in that Big O notation, though?
If you're saying that you want accuracy out to n digits, then there are algorithms with specific complexities for calculating those. But that's still just an approximation, so those aren't any better than the real-world implementation method of simply looking up that constant rather than calculating it anew.
I guess n would be infinite in the limit I'm looking for. I'm looking at this in like a "musing about theoretical complexity" angle rather than actually needing to use or know how to use pi on modern systems.
For the record, I realize how incredibly pedantic I'm being about the difference between the irrational pi and rational approximations of pi that end up being actually useful. That being said, computational complexity has enough math formalism stink on it that pedantry seems encouraged
It's a number and complexity refers to functions. The natural inclusion of numbers into functions maps pi to the constant function x -> pi which is O(1).
If you want the time complexity of an algorithm that produces the nth digit of pi, the best known ones are something like O(n log n) with O(1) being impossible.
as an engineer, a lot of languages (even proprietary ones) have a built-in constant pi variable because it is so ubiquitous - its easier and more readable to use pi than 3........
I've also never seen a fellow engineer simplify pi to just 3, although I have seen a rise of memes from people who think they do.
I would slap someone if I saw them try that, it's unnecessarily sloppy. 3.14 is the default, and trivial to work with if you're using a calculator (I would also slap someone if I saw them not using a calculator). Unless you just LIKE having all your calculations be off by almost 5%. Then you'll come back wondering why so many of your parts are out of tolerance.
As an Astrophysicist, I have never seen anybody use pi=1, you just leave the character, it's anyway better to read, is not like you do any calculations by hand anyway. More common is c=hbar=kB=1, but that is not an approximate, is a gauge in another unit system. Also... Astronomy is not astrophysics...
As an astrophysicist, can you read me my horoscope? I'm a scorpion
Sure, give it to me, I can read it for you.
I use 3 ^16^/~113~
At least do 22/7
(355/113)/ pi = 1.0000000849136...
That's way more numbers to remember than 1/7 above 3
You're a monster. I love it
Only basic math. You can convert Pi even more precise, but I think to 6 decimals is enough.
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