What field do you work in, and how many digits of pi do you use?

nycki@lemmy.world to Asklemmy@lemmy.ml – 128 points –

This article says that NASA uses 15 digits after the decimal point, which I'm counting as 16 in total, since that's how we count significant digits in scientific notation. If you round pi to 3, that's one significant digit, and if you round it to 1, that's zero digits.

I know that 22/7 is an extremely good approximation for pi, since it's written with 3 digits, but is accurate to almost 4 digits. Another good one is √10, which is accurate to a little over 2 digits.

I've heard that 'field engineers' used to use these approximations to save time when doing math by hand. But what field, exactly? Can anyone give examples of fields that use fewer than 16 digits? In the spirit of something like xkcd: Purity, could you rank different sciences by how many digits of pi they require?

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I'm a waitress, and pie is $12.50.

If that's for a whole pie that's dirt cheap. If that's for a slice then that's some expensive pie.

I'm Australian. I normally manage a pie with 5 digits, unless it's particularly crumbly or runny, in which case I will sometimes use 10!

I find this comment absolutely hilarious.

I recognize your profile pic from a comment months back that was also a short, deadpan reinterpretation of the question that I found hilarious. I can't for the life of me remember what it was of course.

Thanks for making me laugh!

I bet all the Americans reading this are now imagining you eating some gooey dessert like key lime pie or pumpkin pie with your hands.

If it's anything like the little island off it's east coast it will be steak and black pepper of a chicken korma pie

Steak and black pepper pie, now that's what I'm talking about!

Peppersteak and Tomato ftw.

Chilli beef and cheese from a servo or gtfo.

I often find chilli beef on the dry side, I guess that it would mean that that pie may need only 5 digits and not the full 10 of a juicy steak pie

With cheese inside its a sloppy mess and often requires the full 10. Though tbh I haven't lived in Australia for 10 years or eaten meat in 20, so I wouldn't listen to anything I have to say about pies.

Fraser Island? Or Tasmania?

The ones slightly larger that tasmania...

Sacrilege!

Firstly 1, 500 km away is not coastal (if it was then the UK is an island off the coast of Iceland).

Secondly if anyone is off anyone else's coast it's the west island which is off our coast, not the other way round.

I'm a liar and I use all the digits of pi.

Well you’re honest about being a liar so there’s that I guess. I on the other hand only speaks the truth and I use all the digits of pi, honestly I do.

There are two guards: one speaks only the truth and the other only lies. But both know the infinite digits of pi and are underemployed as guards who never get to use that knowledge.

I haven't typed the digits of pi for probably 20 years because it's defined as a double precision float in all the programming libraries I use.

Ya know, this thread has inspired me. I'm a sound engineer, and find myself yelling "check one two three four" in the michrophone to test it all the time. I'm gonna start reciting the digits of Pi instead, and then as I learn them, I'll progressively advance how many numbers of Pi that I use in my everyday job :D

I work at a library, though. I should probably just go with poetry or Douglas Adams or something, but this makes me sound much more impressive

Or some Douglas Adams poetry: Vogon poetry.

Oh freddled gruntbuggly,

Thy micturations are to me

As plurdled gabbleblotchits on a lurgid bee.

You are already reciting some of the digits of pi. Just not the first ones.

As a mathematician, I don’t use any digits, but the symbol π.

As a computer scientist, same, but it's called PI.

It's the computer that does the thing with the digits, not me. 🙃

In which case you're probably using a predefined 64-bit floating point number, which I think is accurate to 15 digits.

Well, you know what's funny, after writing the comment above, I double-checked what the π constant is called in Rust, as that's what I'm mostly coding with these days.

And well, it actually makes you choose. There's f32::consts::PI and f64::consts::PI. Which I guess, makes sense. If you're calculating with 32-bit floats, you should be aware that π is going to be less precise.
So, yeah, I'm a hoax, computer scientists do need to decide between 32-bit and 64-bit.

In fact, the one time I needed π in Rust, was as a 32-bit float. I built a tiny gravity simulation in a game engine and game engines generally use 32-bit floats...

I’d like to agree, but writing π with capital letters is heresy.

Yeah, math conventions and programming conventions don't always align. As in, basically never...

I work in healthcare and I've yet to use even a single digit of pi

What are you talking about? I constantly explain the calculus of the flow rate in the push IV drug I'm giving by going through the (pi)r^2 * h of the syringe, with emphasis on the dh/dy. All my patients love hearing it. They constantly thank me as I finish giving them the dilaudid.

Software engineer.. we also use all 16 digits of pi

"all 16 digits" implies that there aren't any more digits of pi, which isn't true. Just FYI.

I am a farmer who has to graft pipe cuts at various angles. i use 3.14159. which is plenty since i am measuring my cuts to the nearest eighth of an inch and i am not sending this ish to the moon.

I would like to hear more about rice farming and if the rice is tall or you are.

hmm rice can get pretty tall. i guess my username should be talltallricefarmer

Retail, and to my knowledge among all my coworkers we have used zero digits of pi.

When I code in C++ I use 15 digits of pi after the decimal point (double float) but I have only rarely coded for money and have never used pi for those work products, so again, zero digits on the clock.

Ditto for restaurant work, although 2 decimal points would be more than enough if I needed the volume of a cake or other round food.

I'm an auditor. Zero digits is the norm if I have to use Pi there is something VERY wrong

I'm a consultant and I use whatever Android calculator gives me

When I worked on a website with a map on it I used 15

50000kms is the kind of distances you get going around the earth so to get it down to a millimeter precision from 50k I think 8 or 10 digits required?

So I just put 15

As an aside, you don't need to/shouldn't pluralize km. It's just 50,000 km. 👍

Software Engineering. 16 sigfigs across 64 bits

Software Engineering too, I just use std::numbers::pi. Don't know how many digits it is offhand.

I use M_PI and generally don't care unless the device acts funny.

TIL a 64-bit float is accurate to 16 sigfigs.

Edit: actually, out of curiosity I decided to try and calculate it. I've very possibly done the wrong calculation, but what I did was log~2~(10^x^)=64, which works out to x≈19. Which isn't 16, but is very close, and when you consider the way the float actually works it wouldn't be too surprising that it was lose some information (the sign bit, for example, is immediately completely lost in this context).

A 64 bit IEEE float has 53 significant bits (the “mantissa” or “significand”), and log~10~(2^53^) is 15.9546.

Yeah I wasn't sure if it would be correct to throw out the exponent entirely or if it might end up contributing some amount to the final accuracy of the number. I hadn't spent a lot of time thinking about the problem.

Yeah the exponent just allows you to represent lots of magnitudes, but it wouldn’t contribute to the accuracy because you basically have 1.xyz * 2^exponent^. So the xyz significand is the only part that counts for significant digits. Although I guess in some sense you are partially right, because the exponent exists it is assumed that the first bit is always one, since otherwise you would just adjust the exponent to the first one, so only 52 bits have to be stored.

As a pilot I can't think of a time I've ever done numbers math with pi. Private pilots are taught to use an E6B flight computer, which is basically a device for accurately drawing and measuring the triangle you're looking to solve instead of doing algebra and arithmetic.

In the wood shop, if I do have to do algebra rather than just drawing a circle with a compass, I'll use 3.14, and I still have to round to the nearest 32nd of an inch.

I'm British, not American, so I use 7/22.

Rub it in, metric π, you imperialist rebel.

Engineering student. I typically use whatever number of digits the calculator gives me in calculator computations, but that's unnecessary. IMO for a design, an engineer should use at least as many digits of pi as needed to not lose any significance due to truncating pi specifically. Practically, this means: keep as many significant digits as your best measurement. In my experience, measurements have usually been good for 3 significant digits.

For back-of-the-envelope or order-of-magnitude calculations where I only need to get in the ballpark of correctness, I'll use 3 (i.e., one significant digit). For example, if I order a pizza with a diameter of 12 inches, A ≈ 36 * 3 in^2 = 108 in^2 is a fine ballpark approximation that I can do in my head to the real area A = 36π in^2 ≈ 113.097... in^2 that my calculator gives me.

I like your idea of using 3 as an approximation to get ballpark figures - if you wanted to add a smidge of extra accuracy to that you can just remember that in doing so, you’re taking away roughly 5% of pi.

0.14159265 / 3 ≈ 0.04719755

Add in around 5% at the end and your approximation’s accuracy tends to gain an order of magnitude. For your pizza example:

108 in^2 x 1.05 = 113.4 in^2 which is accurate to three significant figures and fairly easy to calculate in your head if you can divide by twenty.

You could even fudge it a little and go “108 is pretty close to 100. 5% of 100 is obviously 5, so the answer is probably around 108+5=113”

I'm a programmer and I remember 33 digits, but in practice I never use pi because I never have to deal with geometry

Game programmer here, lots of geometry. Usually 16 digits after the dot is ok. In graphics programming is also useful to define and use Tau (π×2), also defined to 16 digits

I work in trails, like what you might walk on, and in the rare case I need pi, I use 3.14. This week, we have a meeting to talk about some things on 14 March. I will be using cornbread because I do not know how to make a pie but I will eat the pie others make. I look forward to this meeting.

Mostly I'll just go with M_PI.

355/113 = 3.14159292035398 is close enough for my needs.

Answering my own question: I work in web development and my usual value for pi is the standard JavaScript Math.PI. JavaScript uses 64-bit floats, which are accurate to about 15 decimal places. But that's how many digits the computer uses. For practical math, I don't think I've ever needed more than 2 digits of accuracy in an equation involving pi.

Prototyping. I just checked and my slide rule has a notch for pi. So, all of them.

But how many digits of the result do you use?

None of them! Numbers are a poor way to communicate with most of my clients.

On the rare exception, it depends on the number of significant digits of the measurement I (for example) multiply it with. Digits past that don't communicate any useful information.

Structural engineer, and it depends. If I am doing structural or quantity calculations, I can get away with 3.14 (3 digits).

If I'm dealing with survey coordinates defined by horizontal curves, I'll have to use at least 10 digits.

So do I have this right - if you think about the building being structurally sound you can get away with more error than if checking whether you're accidentaly on the neighbour's plot of land?

Not a civil engineer, but an engineer here, if you're doing structural soundness, you usually apply a generous margin of error, so it doesn't have to be that tight, you're building it 3 times as strong as needed anyway.

While if you're calculating where your plot is, you don't want to leave a few meters empty or go past a few meters "just to be sure".

Yes.

There isn't that much benefit to knowing if something is 4.5672% overstressed compared to being 5% overstressed. There are also some cases where the method of calculating demand or capacity isn't that precise; the design code will show the simple equation but have a more complicated equation that better models what is happening in the commentary.

In contrast, some surveying is dealing in a state's coordinate plane. This can be very precise, with some measurements provided down to the 1/10000 of a foot to keep error down when they measure it in the field. In that case, you need to be more precise.

I rarely use pi. But when I do I only use 3 digits. I wish I could use less, but we still need to use change when we make purchases.

Back in middle school I memorized this much of pi (for no good reason):

3.14159265358979323846264338327950288419716939937510

That’s far more accurate than I’ll ever need.

The digital field, and we use the first ten digits, especially when those first ten digits is some person's password with the password hint "easy as pi".

This probably won’t play well with this audience, but I’m a management/strategy consultant. “~5” (technically one decimal place but also rounded to the nearest interval of 5) for any C-level decks ;)

That's less than one significant digit! Even just to one significant bit, pi is 4.

Chip R&D. We only use 1's, 0's if management is feeling generous. There are no circles, no need for pi.

I don't use Pi but I do use GPS fairly often and try to get down to 7 digits after the decimal point. Our equipment probably isn't quite that accurate though lol so the seventh digit is likely a guess. Probably even the 6th digit.

Well I’m an uber driver and I’m requesting you start using 9 or 10 digits because my passengers are all over the place when I’m supposed to be able to see where they are.

In Biostatistics - only ever use pi in the variance of the logistic density. Using 3.14 gives substantially equivalent results to using arbitrarily large precision. But I use whatever my calculator or R give me.

Equipment engineering. Usually 2 if I'm doing math by hand. 5 for more accurate calculations.

I can't say "professionally" but I learned CAD design with FreeCAD, and know the topological naming issue thoroughly.

Almost all "mystery" problems in CAD are due to a combination of the hacks that get around the Topological Naming Issue and π.

In CAD, you cookie, you brownie, you might even salad, but you stay the hell away from importing π as a reference on anything complex. For 3D printing, I never need better than 0.05mm so 3.1416.

Mechanical engineer here - Matlab uses 16 digits for pi(), so that's my go-to. When doing some larger thermodynamic simulations, I sacrifice some digits of pi to get more computational headroom. But that's only after I get really annoyed at the code, and it almost never helps (but rarely hurts, as well)

I work in the Bakery field and our specialty is Pie.

Embedded engineer, working in education. I use 3 for mental estimations and whatever is stored in the calculator, I have happened to grab, for "precision" work. Sometimes I'll even round pi to 4, to build in some tolerance when calculating materials.

I'm a nothing in particular, and I used to remember 100 digits. I could probably remember again in an hour.

Well, I have two answers. If it is mental math I use 3.1 and round up. If I am calculating something I care about I use my TI-86 which has pi to 14 digits.

Practically speaking, I don't often need to convert diameter to circumference but I do occasionally need to calculate area or volume and in those cases I have way more error in other measurements or assumptions (2 or 3 digits) so 5 digits of pi is more than enough.

Why would anyone use this fakenass number it makes no sense

if you round it to 1, that’s zero digits.

Isn’t rounding to zero digits a nonsensical concept? And “1” is one digit, not zero digits.

Isn’t rounding to zero digits a nonsensical concept?

Mostly, yeah. But sometimes you really just need to know the order of magnitude, which is a process kinda similar to rounding, but does lose a digit in the process, so you could kinda argue—if you squint a little—that it's "rounding to zero digits".

That's basically my reasoning, yeah. Specifically, in floating point notation; if you get rid of all the mantissa bits, you'd be left with 1 * 2^0. I suppose it could be 0 * 2^0, but a leading 1 is implied, since virtually all numbers are nonzero.

Small correction: Pi lies between 2^1 and 2^2, so its floating-point exponent is 1. With all the mantissa bits cleared you'd be left with 1 * 2^1, not 1 * 2^0.