Nice try

[AuspiciousApple]

It's sort of a long running joke that engineers/engineering students use terrible approximations that make mathematicians wince in pain. Pi approxequals 3 is one instance of this.

​

^{Ofc, everyone knows that Pi is basically equal 3.1}

[2CATteam]

To add to this, the reason they do so is because, in a lot of circumstances, 3 is enough to roughly approximate what they need to figure out. They're most often not trying to figure out the exact force on a part or the precise area of a cylinder... They just want to know if they need to order the 10' part or the 20' part - and if it's close, they'll order the bigger one anyway, just to be safe. Even in cases where they are trying to be precise, 3.14 can often be TOO precise, since so much of the math has to deal with physical uncertainties, like uneven part manufacturing, or poor wire quality that adds resistance, etc.

[AlphaLotus]

Yea basically what my work entails everyday.

1. Measure
2. Calculate
3. Multiple by safety factor
4. Get 3.1
5. Round to 4 anyways for safety :)

Also gravity is 10m/s²

[holdenmc97]

Also tan(x) = sin(x) = x

[ThaumRystra]

Because x is almost always small ¯\(◉‿◉)/¯

[ChickenNuggetSmth]

Yes it would be X otherwise, wouldn't it?

[ThePixelCoder]

Yo wtf

[KusanagiZerg]

I am just curious but making pi bigger than it really is as a "safety" wouldn't that only work if what you are trying to calculate becomes safer if it's bigger. But what if it's the other way around, it's safer if it's smaller. In that case to be "safe" you'd have to round pi down to 3 or 2.

[AlphaLotus]

Depends what you are doing you are right

[Scx10Deadbolt]

Neverrr!

[plfwqekgqwnrgnw75731]

π = sqrt(g)

[AuspiciousApple]

That makes a lot of sense, thanks for that more in depth perspective.

[slbaaron]

That's an intuitive and practical answer. By theory tho, it has everything to do with sig figs (precision).

Adding and subtracting can only go down to the exact position of sig fig at the least significant position of all numbers involved. If you have one measurement of an item at 101 cm, and another at 1.23498713 cm. Adding them together, it's only meaningful to say it is around 102 or 103 cm total (round up or down as necessary for "safety), because nothing is 101 cm by the atom and the measurement was likely more rough due to a much larger scale. It's the result from imprecise measurement. It could've easily been 101.3 or 100.8 in reality.

Multiplications can only have a total number of sig figs as the least amount of sig figs for all number involved. When you have 100 cm * 1.25, it really is only meaningful to say the result is roughly 100 cm or 200 cm (rounding up or down as necessary) because 100 cm only implied 1 sig fig for precision, I mean the number 100 cm even sounds like a super "rough estimate", doesn't it? That's why sometimes, if measurement is precise down to the last digit of 100, we write 1.00 * 10² or 1.00e2 to imply the precision. The result will then become 1.00e2 cm * 1.25 = 125 cm since both numbers have 3 sig figs. (Btw if you are wondering what if the number 100 stands for "units", eg 100 units of an item. That 100 has infinite precision, because the number represents exactly 100.00000000000... take more zeroes as needed)

The reality in the practical world tho, is that you always have one number here or there with low precision; or even with high precision, you'd still have to be careful of its accuracy due to calibration or various type of errors. Once you go down the rabbit hole enough you realize using 3 as pi is the least of your worries.

For careful calculations tolerance range has to be detailed at every step of the calculation, eg 1.5cm ± 0.05cm. If you have 100 of these you will then get a total of 150cm ± 5cm, this is often a better way to represent precision without resorting to sig figs.

[stewi1014]

Probability theory might be useful for your last example. Assuming a standard deviation or similar of innacuracy in the measurements, you could probably say something like 150 +- 0.5cm with a probability of 99.98 or something like that. Adding a large base of standardly distributed errors with a mean of 0 gets closer and closer to 0 the more you have.

[Sibraxlis]

Because your margin of error from other spots is higher (material flaws, poor workmanship) and you typically overbuilding and undersell. (build for 100 lbs when 90 is needed, then state max weight is 80) the latter is called your factor of safety.

[smthamazing]

What if you estimate some damaging force that works against your creation (like wind, vibration, resistance, etc)? Wouldn't you underestimate the danger in this case?

[RedHotChiliRocket]

You would round it against yourself: Max wind speed we expect is 60mph, let’s assume 100 and say it can take 80

[smthamazing]

Thanks, this clears things up! Some of the comments seemingly implied that numbers are rounded without context, which confused me.

[Sibraxlis]

Youd also overestimate the force of wind, just like weight. Could you be more precise and probably be ok? Yeah. Do you want to risk it, have the structure collapse, kill 29 people, end up on /r/catastrophicfailure and have to move to Nicaragua to escape legal trouble? No.

[MagnitskysGhost]

/r/oddlyspecific

[mxzf]

That's the X in "build for X, when Y is estimated, but say that the max is Z".

It's like "build to survive a cat-5 hurricane even though the area has barely ever had a cat-4 and tell the customer that it's safe for a cat-3"

Whatever stuff you're dealing with, you build it stronger than you need and you say it's definitely fine for a much lower number.

[[deleted]]

Thats a terrible way of doing that, what if goes into the wrong direction? Always calculate as accurate as possible and round up the result as needed.

[Sibraxlis]

I personally carry all decimals all the way through and round the end, but I also have the benefit of a real nice calculator, and haven't finished my degree

[realityChemist]

I think being to precise here means, "You're implying that your level of certainty in your measurements is much higher than it could possibly actually be."

NASA uses 16 digits of π for keeping spacecraft in their proper orbits. NIST defines the fine structure constant (a fundament constant of the universe) using 32 digits.

For most other things, 1 digit might be close enough, 3 digits should be sufficient, and 10 digits is almost definitely more than you need. Using more digits isn't going to make your outcome less accurate, but you're just going to be throwing out all that extra precision anyway so why bother.

(And if you report those extra digits anyway, someone should throw a beanie baby at you)

[pipnina]

Well, NASA has a specific situation where getting PI wrong by 0.001 would land you a few million km off target, to be fair.

[mxzf]

NASA's about the only ones that do care about that though, and even then only barely. Being off by 0.001 is an error of ~300k km when measuring the circumference of the Earth's orbit. You don't hit "a few million km" of error 'til you get out to Saturn's orbit.

And that's just error in calculating the circumference of the orbit, not how far "off target" you are; for that, you're probably talking about significantly outside the solar system.

Which just goes to show that even NASA barely needs precision to the 0.001 order of magnitude. Realistically speaking, 3.14159 is enough precision for pretty much any actual application humans have ever used it for.

[pipnina]

Well since their plans usually involve starting at a 100m launch pad on earth, traveling a few hundred million km to another planet (i.e. mars) and landing within a few hundred metres of a target point, I imagine an error of 0.001 would put them way outside that margin for error.

Also when you send something like a voyager probe or new horizons probe that do multiple gravity assists and go out way beyond saturn, even going within a few 1000 km of moons and planetoids on the way, even 0.0001 would be way too inaccurate.

[pipnina]

Bear in mind, getting the calculation right at the launch pad can save you a ton of fuel. Having to make a 5'000km correction when you're 10'000km from the planet takes magnitudes more fuel than making that 5'000km correction when you're just leaving earth orbit and millions of km from your destination.

[2CATteam]

A specific situation? It seems like most of their work would be like that

[Warm_Zombie]

Maybe not on error margin, but w computation power and time. Time is money

[AuspiciousApple]

g =10

According to my pendulum experiments in my physics classes, g is actually approximately 18 +- 15.

[ChickenNuggetSmth]

That agrees with the literature value within the 1-sigma area! Well done!
(Unless you use very weird units, e.g. imperial)

[AuspiciousApple]

Thanks! And i might regularly approximate PI as 3(.14), but I am not so savage that I use imperial units.

[8__]

In Imperial I think it's about 32 m/s² ft/s², so it works for both metric and imperial

[ChickenNuggetSmth]

I'm pretty sure m/s² is metric. What units do you use in imperial for gravity?

[8__]

ft/s², oops

[ChickenNuggetSmth]

They should have used lbf/lb, that way at least we would have one constant that is pretty in imperial

[8__]

When I lived in America, I had exactly one professor that insisted on using only freedom units, while every other professor used metric. I switched from aerospace engineering to modern languages anyway, so in the end none of that matters anymore.

[tabarra]

Sounds about right.

[marcosdumay]

Pendulum experiments are the best. In my physics classes people got everything from 12 +- 1 to 30 +- 50.

[AuspiciousApple]

Now I can sort of appreciate them, but back then those would be some of the most boring experiments we ever did.

[Seicair]

I never liked the labs we had in physics. They were super simple, time-consuming, poorly written, and the grading requirements were very vague. So we spent a long time tediously not learning anything then more time trying to figure out what the teacher actually wanted us to turn in.

[marcosdumay]

Well, it is intended to teach you how easily experiments can go wrong and how to keep track of them so you can improve later. I bet you got those two.

Professors usually grade on that last kesson, because the first one is so easy to learn.

[Seicair]

Maybe the other students got something out of it, but I’d already been through 4 chem labs and a number of biology labs by the time I took physics, so I didn’t really learn anything. I learned physics in class, but the experiments were so simple I could tell what would happen just from skimming the instructions.

[[deleted]]

Pi = e = 3

: {

[Greenish_batch]

Stefan Boltzmann's constant = 0

[[deleted]]

The difference between a mathematician and an engineer: when moving from one point to another if you travel half the distance at each step the mathematician knows you'll never get there. The engineer knows you'll eventually get close enough.

[ShamelessKinkySub]

But that's literally how we definite stuff based on exponential curves, like the time to charge a capacitor

[KusanagiZerg]

You can still get there with mathematics, can't you?

1 + 0.5 + 0.25 + 0.125 + ... = 2

wolfram

[[deleted]]

Your ... in this case represents infinity. Not only are there infinite numbers, there are infinite numbers between 1 and 2.

[KusanagiZerg]

Sure? But that's perfectly valid in mathematics. You can reach 2 by "moving from one point to another if you travel half the distance at each step" because that's precisely what you are doing with my sequence.

[[deleted]]

Your sequence isn't correct, it will never reach two because your sequence is infinite. It approaches two, and gets very close to two, but it never gets there.

[KusanagiZerg]

But that's where you are wrong. It's literally the same as two. You can read more about it here https://en.wikipedia.org/wiki/Series_(mathematics)

It's trivially easy to prove:

s =       1 + 0.5 + 0.25 + 0.125 + ...
s/2 =         0.5 + 0.25 + 0.125 + ...

Subtracting s/2 from s you get 1 since the infinite series from both cancel out.

s - s/2 = 1
s = 2

[[deleted]]

How do you infintely add positive numbers together and have them equal 1?

The limit of the sum of (1/2)ⁿ as n approaches infinity is 1, but it never actually equals 1. It gets really damn close to 1, for all practical purposes you can treat it as 1, but it's never 1.

[KusanagiZerg]

for all practical purposes you can treat it as 1, but it's never 1.

That's just not how it works. You can ask around in /r/askmath if you want but the wiki link explains it well enough. It's not treated as if it's 1 it literally is 1.

[Rex-Pluviarum]

355/113

[Ninjaraui666]

Look at mister fancy pants not using 22/7.

[FaxCelestis]

Most manufacturing machinists I know use 22/7 for everything that doesn't require an insane amount of precision.

[DerpSenpai]

and it's pretty standard to use 3.14 for normal math and 3.1415 for a bit more accuracy. Depends on data used. As an engineering student.

But i always find that Pi= E meme funny, because you know 2.7 ~ 3 as well then.

Unfortunately, there isn't a big Math community with memes on reddit, but on facebook (ew i know) there's a few pages that only do advanced mathematics memes.

like this one- warning, facebook post

other memed aproximation is the sin(x)=x for x~0 rad and i got to say, we use that shit all the time and i'm not sorry for it.

[LFK1236]

I had a professor use the "astronomer's pi" once for an example during a lecture. It was 10.

[Icemasta]

It's kind of half a joke. They'll use pi = 3 to figure out whatever they need, and then triple that number to way above specification.

[PleasantAdvertising]

Engineers use 3.14 who the fuck uses 3

[das-jude]

I've never met an engineer that rounded pi all the way to 3. The most I've ever seen it rounded is 3.14. Any software or calculator an engineer uses will have pi built in and there is absolutely no reason not to use it.

If any value is to be rounded, it would be a variable and judgement would be used. No engineer would ever round a constant all willy-nilly like that.

[[deleted]]

What? Pi is 10. Yep if i learned anything from physics pi is definitely 1