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?
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”
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.
That’s a crime 😭
Oof :D
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 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.
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.
If that’s for a whole pie that’s dirt cheap. If that’s for a slice then that’s some expensive pie.
Damn that’s pricey
Not if it’s a whole pie.
…
That is a whole pie, right?
Worth it
I’m a consultant and I use whatever Android calculator gives me
Molecular biology. 4 digits.
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.
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.
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?
No I round the result to compensate for the error.
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
