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”
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Pi = 355/113
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/
From the article for anyone who cares, NASA uses 15 digits (
3.141592653589793) because at Voyagers current distance from earth (~48 billion kilometers) that would give you an accuracy of less than half an inch.
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:
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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.
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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.
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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.
I was surprised so I did the computation just to resolve the disk of Betelgeuse at 550 nm, and I found a telescope of 2.8 m, that’s definitely already doable. We already have 8 m in one piece and 10 m segmented, JWST is 6.5 m segmented. The ELT is planned to be 39 m for 2028. So this star is closer and bigger than I thought.
And these are the images we have from one of the top imaging instrument SPHERE on the VLT in 2019. It’s precise enough to show the change of shape due to its variable star type.
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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.
It’s called “cheese cake” not “cheese pie” so I don’t think so
Not according to her. And I ain’t about to argue the point with her…
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
The last 4 years of my working life, I taught some math in my small rural local school. I introduced a tradition of calculating Pi from scratch by various “silly” means. All shamelessly stolen from Matt Parker of Standup Maths fame on Youtube. The students, (4th through 8th grade), were always highly entertained and may have accidentally learned some math…
When you least expect it, Pi is there.
Love Matt Parkers videos, makes math more fun, great to share it with the kids.
Electrical engineer. Never used 3. Always 3.14. don’t really get the joke.
I just use the pi from my calculator or numpy/matlab. But I’m often too lazy for vacuum speed of light and use 3e8 m/s.
Electrician over here is killing the buzz
Electrical engineer. I’m nowhere near as useful as an electrician.
I’ve seen some blueprints who use 3.5. I guess it’s close enough but definitely not too small
Strange. If you’re going to use a decimal point, why not the right one?
You are correct, I used the wrong one for my region but according to Swedish Wikipedia (bad source) the US and UK uses a . If that is incorrect I’m happy to be corrected!
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…
And then you’re using C++ and they scold you for including cmath for just M_PI because it increases compilation times.
We’re talking about engineers here! We’re using MATLAB or Python if we’re programming at all.
Your not writing regular python code, your writing a special subset of python intended for engineers and scientists called “bad python code”
My code is not intended to be run by any idiots but myself! Anyways why can’t i make sense of what i have written just a month ago?
Your not writing
Coder/engineer confirmed.
As a comp sci that interacts a lot with engineers, I feel this in my soul.
You can’t say that for all engineers. I’m one and the biggest part of my job is programming in C++
Just wanted to say something similar. Any low latency high frequency code is written in c++, c or assembler. And that’s engineers work usually.
[glares in rust]
Still want to try rust but in my field it’s just not established enough unfortunately. But I love the idea of the language.
honestly, my rust comment was mostly a joke; rust is great for it, but its readability is really bad. i’m not a huge fan of writing/reading it, just using it.
As they should, if that’s the only thing you are using it for, don’t introduce a whole header file, just put the following in the constants.h or equivalent that the proj for sure has:
#define M_PI 3.14159265358979323846264338327950288Yes, it’s literally what math.h has defined.
If I’m not completely mistaken M_PI is not part of the C standard, so depending on your stdlib or compiler or even compiler flags you will have to define it yourself even in C.
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.
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
“Modern” is a bit misleading, x87 had
fldpi. The whole x87 part of the standard has been deprecated with x86_64 in favour of the whole sse series of instructions and those don’t come with pi. You instead load a constant from program memory, just like any other.As processors (as of yet) still support those legacy modes they will also contain the constant somewhere in probably microcode storage, calculating it on the fly makes literally no sense at all: It’s (for x87) 80 bits of data, much shorter than any imaginable program, smaller than any circuitry able to compute it so you’d be spending time to save no space which is pointless.
ARM, RISC-V etc. come from the RISC tradition so they wouldn’t be caught dead including such an instruction. Both have zero registers though as zero is an absurdly useful constant, simplifying things drastically, both on the hardware front as well as within the instruction set (move is add zero to source, save to destination, clear is add zero and zero, save to destination)
Now, that’s finite constants. In particular, it’s about floating point arithmetic, which is a wonder of maths and a deep rat’s nest of numerology, but has finite precision, it’s not true real arithmetic. Real real arithmetic is undecidable, in particular comparison and expansion to decimal form are undecidable. Printing infinite strings of digits is usually not what we want to do, and limiting precision of comparisons is… not ideal, but better than having limited precision at every operation: You can decide once you’re comparing how accurate you want things to be and don’t have to worry while writing down your formula (btw Herbie exists, and that’s why packages like this exist. In that case pi is not a constant but a formula, which can be expanded as needed. Quite slow compared to floating point hardware but when you need it you need it and even if you don’t it’s still useful as a sanity check, gives you an idea of how far off the floating point results are without having to call in a favour with a mathematician.
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.
It’s usually a constant (or several ones with varying degrees of accuracy and size)
It all depends on the precision you need. You could use an infinite series to get to the precision needed but for most use-cases it’s just a double baked into the binary itself, hence O(1)
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.
“is not like you do calculations by hand anyway”
… get off my lawn, whippersnapper.
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.
I heard once π²=10 is fairly accurate approx and thus g=π²=10 in astrophysics where people thinks in order of magnitude, not value.
But my engineering ass is telling assumptions with larger than 50% difference from actual value may cause issues on order of magnitude if the value is used multiple times and isnt it better be like 5=1/2×10?
That’s because your engineering ass needs things to be physical and sane. Physics is a field for the mentally unwell to sink further into insanity while incoherently scribbling greek letters on every available flat surface.
On a more serious note, yeah you absolutely have to be careful about where you apply really ambitious simplifications like that. There are plenty of mathematical regimes where you can use natural units (this is the term to look up if your interest extends further) and simplify your reference frame by a hell of a lot though. Setting the speed of light to 1 is also a hell of a drug, and brother I’ve got an addiction
They do? Why not provide some explanation?
Somebody else already said it, but that’s what the title is.
Longform: a lot of calculations that happen in astro deal with distances so large so large that only order of magnitude changes actually meaningfully affect the end result. To connect to a more common topic, here’s a joke.
“Whats the difference between a million dollars and a billion dollars?”
“About a billion dollars”
This joke works for the same reason; 1 billion is so many orders of magnitude larger than 1 million that (1,000,000,000 - 1,000,000 = 1,000,000,000) is only incorrect by ~0.1%, even though substituting 0 for 1 million in that equation seems ridiculous on the face of it. Substituting 1 for pi has similarly minimal errors (tbh it usually matters waaaaaaaaay less than .1% error) in a lot of astro math
Also how you get classical physics from relativity.
Astronomy often has pretty high error bars on their measurements (distance, size of stuff, etc).
In astronomy, the important part of the number is often just how big it is (that is, the exponent). Multiplying by pi doesn’t change much in that.
The explanation is in the title.
It isn’t an explanation
So this is just an Ai produced meme?
“Everything I don’t like is ai”
Grow up. The imgflip watermark is clearly visible in the meme, and it’s an ancient meme format.
This image is a two-panel meme utilizing a blurry, chaotic photo of individuals seemingly engaged in a mock fight and a separate photo of a person appearing to conduct a science experiment with a small flame, possibly under the influence of poor judgment.
In the left panel, the text “MATHEMATICIANS DEFINING PI” is superimposed over two individuals engaged in a dramatic physical altercation, one holding the other back. A third person, who is uninvolved but present, is labeled “ENGINEERS JUST USING 3 BECAUSE IT’S WITHIN TOLERANCE.” This suggests a hierarchy of concern regarding the numerical precision of π (pi), with mathematicians caring deeply, engineers demonstrating relaxed standards, and general chaos ensuing.
In the right panel, a shirtless person crouches and conducts a questionable experiment involving a lighter and a small pipe. The caption “ASTROPHYSICISTS” is positioned above their head, and below is the phrase “PI = 1.” This implies a level of approximation so extreme it borders on parody, indicating astrophysicists allegedly use such simplifications in the name of cosmic-scale practicality.
The overall composition is an exaggerated commentary on varying standards of numerical precision in different disciplines, presented through low-resolution imagery and humorous juxtaposition.
