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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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 had to upvote this comment for its pure sincerity.
I work in the Bakery field and our specialty is Pie.
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”
Why would anyone use this fakenass number it makes no sense
I’m a consultant and I use whatever Android calculator gives me
Molecular biology. 4 digits.
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.
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.
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 ;)
Oof :D
That’s a crime 😭
That’s less than one significant digit! Even just to one significant bit, pi is 4.
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 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.
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.
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.
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)
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.
So you round up 3.1 to 3.2?
