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 consultant and I use whatever Android calculator gives me
Why would anyone use this fakenass number it makes no sense
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.
3.14159
Design of mechanical parts, specifically machined. 0.001" is a fairly tight tolerance for my applications, 0.0001" is going to cost a pretty penny and is used judiciously. We don’t really need to go to 3.14159 but I honestly think we do because it rhymes.
That is 0.025 Millimeter in normal units
You can say 25 micrometers
Yes, it’s technically correct (which we all know is the best kind of correct) and engineers would understand.
Using mm means most everyone (who knows metric) understands that in much more practical terms. A quarter of a tenth of thiiis much is a pretty damn tight fit.
Bold of you to assume that anywhere close to everyone who understands metric would know that 0.25 is a quarter of something.
Bold of you to assume that the country that still uses the Imperial system is the one that better understands fractions.
I didn’t say that imperial countries understand them better.
Micrometers is actually so common that it has a colloquial non-SI name of “micron”
According to wiki:
The micrometre is a common unit of measurement for wavelengths of infrared radiation as well as sizes of biological cells and bacteria,[1] and for grading wool by the diameter of the fibres.[3] The width of a single human hair ranges from approximately 20 to 200 μm.
This
because it rhymes.
With?
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.
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.
Chip R&D. We only use 1’s, 0’s if management is feeling generous. There are no circles, no need for pi.
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.
The State of Indiana tried to define it to 1 digit by law.
https://en.wikipedia.org/wiki/Indiana_pi_bill?wprov=sfla1
Thankfully, the bill was never passed.
Usually 8 decimal places.
But I work in HASS so we don’t have much call for pi.
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 Australian. I normally manage a pie with 5 digits, unless it’s particularly crumbly or runny, in which case I will sometimes use 10!
3628800?? thats a lot!
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’ll be here all year :P
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
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.
true enough
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
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 log2(10x)=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 log10(253) 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 * 2exponent. 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.
Isn’t it just 15 significant figures then?
I would round up to 16.
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)
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.
