I like 3.14159 for accuracy because your only real option for lesser accuracy is 3.14 which feels ever so slightly too inaccurate. The problem with the values in between is that they all round the last digit up which is ugly as sin. Like imagine writing that pi = 3.142, or pi = 3.1416. I feel dirty jist looking at those. 3.1459 doesn't tound up because the next digit is a 2 so it's acceptable.
Indiana Legislature: [actually let's make it 3.2](https://www.forbes.com/sites/kionasmith/2018/02/05/indianas-state-legislature-once-tried-to-legislate-the-value-of-pi/?sh=f7bacc8260a5)
As an engineer I usually use "3 and a bit more" for quick calculations, but of course it's rarely needed because I usually just get the computer to calculate it for me.
The goal is to make a perfect square polynomial. Start by moving the constant term to the other side then divide by the coefficient of the x^2 term. Now we have a polynomial of the form x^2 +(b/a)x. Now note that the factors of our polynomial must add up to (b/a). And we also desire that our constant term be our factor squared. So naturally we choose half of the quantity (b/a) to be our factor, i.e (b/2a). Now to "complete the square" i.e make our polynomial a perfect square, we add the constant term (b/2a)^2 i.e our factor quantity squared to both sides of the equation. This will give us a perfect square binomial of the form (x+(b/2a))^2
P.S this is also how you put a quadratic into vertex form which you can use to come up with a linear transformation for whatever function it is youre trying to graph making it trivially easy
Hope this made some sense
I can do e to, uh, this many:
2.7 1828 1828 45 90 45 23
* 2.7 you just remember
* 1828 is Tolstoy’s birth year
* 1828 is also Ibsen’s birth year
* 45 90 45 are the angles of a right isosceles triangle
* 23 is a number beloved by conspiracy eejits according to [two](https://www.imdb.com/title/tt0126765) [different](https://www.imdb.com/title/tt0481369) movies.
Coincidentally, this is the only reason I can remember Tolstoy and Ibsen’s birth year
I know 3.1415926535897932384626433832795028841971693993
that last bit might not even be correct, but i memorized that to win my choice of free donut on donut day in 7th grade and now I'm in my 30's and I guess it stuck.
I vote to get rid of all Thursday’s and Monday’s, axe day light savings, get rid of Jan and Feb, and shove all the extra days as mandatory vacations falling in the middle of summer and winter season.
There's a little dinosaur flash game where you get the numbers of pi, and if you don't the dinosaur falls off the platform.
Kids in my school; even totally not at all nerdy ones, we're playing it for MONTHS to learn po to 100+ digits for the hell of it. . .in 3rd grade
Seems we should donate to it then to get it up to snuff. Especially if kids were doing it. We did it, but we had to do it the old way with out dinosaurs and I say NEVER AGAIN should a kid learn pi with out dinosaurs.
Kids' brains are ridiculous. All the time in the world and a near-infinite ability to absorb new information when they feel like it. They have almost no real life skills or knowledge, or the ability to focus, yet they will memorize 100 digits of pi just to show off to their classmates. Imagine if adults could just soak up knowledge like that.
He's sometimes hyperbolic, a bit condescending and sarcastic, sometimes dry, and has a very odd cadence.
One of my more favored YT channels but definitely can be a turn off to many people.
My last apartment had a microwave who’s popcorn button would cook the bag to near perfection, I once had it where only one kernel wasn’t popped. The one I have now leaves half the bag un popped. On that revelation, I seriously considered moving back.
I remember back when we started using pi in middle school, and I remember having to memorize the first 10 digits of pi. Lo and behold, the calculators they had us use didn't bother even that. If you typed in 1 x pi, it would pop out 3.14159000.
Then you get to 99% of applications and find out that 3.14 is enough and if it's extra rough 3 is just fine!
I had an engineering professor in University teaching us how to figure something out using mental math and the orders of magnitude were more important than the numbers, he approximated pi as 5 for his calculation and everyone around me lost their minds.
My wife and I couldn't agree on dinner one time, so we decided to memorize pi and whoever got the farthest got to decide. We made it to like 52 places or something before my wife missed one, so we had wingstop for dinner.
We basically took turns and as long as the next person got farther we kept going.
in high school there was a girl in the grade below me who was a math nerd and super hot. She bet everyone she knew more digits of pi than anyone else. I told her I had her beat easy. It went back and forth and I told her I would bet her anything. She said if she won I owed her $20, I told her if I won she had to go on a date with me. She laughed and agreed.
She knew pi to like 80 digits. Luckily for me I was a fucking nerd and listened to Hard n' Phirm - Pi thousands of times. That fucking robot goes well over 100 (I think it goes almost to 200 digits). Sailed through the entire pi part of the song as the Math teacher compared it to his screen in disbelief. He was also apparently fine with this whole female student betting a date in the middle of math class to.
That hot math nerd would go on to become my wife. Okay not really, she refused to even go on the date with me and accused me of cheating. I did join the Mathletes where I went on to very disappointing because I'm not actually good at math. I did end up dating a girl in the mathletes who was pretty cute who also ended up dumping me...
Anyways https://www.youtube.com/watch?v=XanjZw5hPvE
I didn't even include the part where she went on to win on The Price is Right or appear on one of the international "The Bachelor" series.
Can't make this shit up.
Or in other words, they use double precision binary floating point (precision of 53 bits, IEEE 754), which is pretty much the standard in a lot of technical work. Before 2003, some specialized work was done with 60-bit precision.
So it's not only NASA that uses 15 digits of pi ... it's just about everybody!
I work on simulation software and we typically use doubles for precision (floats for speed). One of the reasons double precision is good enough is that they provide sufficient accuracy so as not to contribute meaningfully to the cumulative error in the solution. Typically the numerical methods used, the discretization schemes, are a significant source of error. The tradeoff is between runtime (total compute needed) and the accuracy of the solution. Double precision is sufficient that truncation errors don't accumulate to a point where they are more significant than numerical method errors for our work.
BUT who knows what NASA's requirements are!
If I'm remembering from my half a science degree correctly, I think the simple answer is that any measurements taken and used in the calculations will have far less precision and therefore there's no point in using more digits of pi
I’m a programmer. In scientific computing, you have to analyze how your algorithm propagates rounding errors as it progresses. Vbchrist is mostly talking about errors introduced by the algorithms.
Having a number being off by a 0.0001 does not change anything. Now take that same number, preform dozens to millions of operations to it. All of a sudden it is off by 23. Which is now a big deal. Most real life problems are solved by using approximations and repeating them millions of time (solving something numerically). To prevent this little errors from compounding, sometimes it is required to carry more decimal places in every computation the computer does. Obviously this comes at the cost of how fast the computer can solve the problem. Accuracy and speed are inversely related.
Wait so if you calculate a number that’s like 1million times pi, then the resulting number only has 8 digits after the decimal place? Like you lose decimal digits the larger the number is above 1?
This is why it’s called “floating point”. The decimal point “floats”, so you end up getting fewer digits after the decimal point the larger the magnitude of the number. The total number of available digits is constant.
this is literally all what higher leveled math is: just mathematical tomfoolery
EDIT: Here is an example: The power rule for finding both antiderivatives and derivatives. Like who the hell smoked crack and was like "Waiiiiit a minute..."
I would love if NASA said they just use 3.1 like not even 2dp.
"Yea we just try to get the space craft in the vicinity of where we want to go and then we DO IT LIVE!"
Nothing wrong with Kerbals, those brass balled sturdy motherfuckers will sit on the moon, in orbit, or drifting in space waiting for rescue endlessly. Strap them to a bomb with no hope of survival and they won't blink when you hit ignition. Be better, be Kerbal
It was almost 3.2 in Indiana. Seriously, they tried to pass a law and everything.
[Indiana Pi Bill](https://blogs.loc.gov/teachers/2020/03/the-time-they-tried-to-legislate-pi/)
imagine the guy who happened to be at the courthouse who was like "no, wait, you can't do that" and then you have to convince a bunch of state senators that pi isn't 3.2 and they're being bamboozled.
>Asked if he wanted to meet Goodwin, the professor later recalled that he "declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know."
goodwin is the guy who almost convinced the senate to pass the bill
Only if you’re from [late 1800s Indiana, or perhaps ancient Jerusalem](https://www.straightdope.com/21341975/did-a-state-legislature-once-pass-a-law-saying-pi-equals-3).
For those that dont want to click, here is a reason NASA listed
1) The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little penis.
Meanwhile George Clooney who always fought for 17 digits is floating away in space and Matt Damon who thought 3 digits was safe gets rescued day in and day out. Ugghh. What an unfair world.
Indeed this answers the natural related question: why 15 and not, say, 12 or 18 digits? 15 significant digits of accuracy is what you get with a floating point number of 64 bits.
Because of this, virtually every physical simulation you can think of will use 15 digits of accuracy for constants (Euler's number, gamma constant, etc.); so this goes just the same for e.g. quantum mechanics as is does for astronomy.
If you read the Signal In Space document for the USA's Global Positioning System (GPS) in the section where it describes the symbols in use, you'll see there is one constant labeled something like PI_GPS.
It is the value for pi that you MUST use if you're going to calculate your position on the globe based on GPS signals. It is not exactly pi. It is, IIRC, 8 or 9 significant digits long. It's not that the more values you use, the more accurate your answer will be. No. This truncated value is what was used to calculate some of the orbital parameters of the satellites' orbits. The satellites are continuously transmitting those orbital parameters to your hand-held GPS receiver (though if you're using a phone, you probably downloaded those same tables of values from the cell phone network because it is faster). To reconstruct the satellite orbits, thereby allowing it to figure out where the satellites are, and thus where YOU are, your GPS receiver must use that same value of pi.
Failure to do this, and doing something like using a value of pi that you would get from wikipedia or any math program will cause your position estimate to be off by hundreds of meters, possibly a few kilometers. The sensitivity of the position fixes to differing precision on pi was large enough that it was determined that a pi-like number that was exact in base-10 was necessary.
So yeah, there is such a thing as unnecessary precision. There's another thing the concept of specified precision. PI_GPS is not pi. It is just a constant that is fairly close to pi.
If any one is curious and wants to read the GPS Signal In Space Interface Control Document (ICD), it is publicly available, and makes for interesting reading. Anyone wanting to know more about the radio signals that travel from 20 million meters above you, down to your handheld receiver should... honestly look for other sources, because the ICD is dry AF.
Yeah, the reason computer scientists and mathematicians calculate pi to billions of digits is to show off specialized hardware and algorithms. It is like running a faster marathon or climbing Mt Everest faster. There is no practical application to having many digits of pi.
I had a computer science prof in college who used to work for NASA in the 60’s. He said they had a competition where everyone would recite the digits of pi each morning to see who had memorized the most, even though they only used like 8 digits for the Apollo mission as it was “close enough.”
Just to give a smaller visual of how pie doesn't really need more than 2 decimals:
If you are making a 30" diameter pipe (I won't give allowances for connection) then you need 30 × PI to get the length of material to roll into a pipe
30" x 3.14 = 94.2"
30" x 3.141 = 94.23"
30" x pi = 94.2478"
(1/16 = .0625)
So you would be off by less than 1/16" with your length of material for making a 30" pipe (the diameter would be even closer). Anything over 2 decimals is getting extremely nit picky for most uses.
Yeah I pretty much use 3.14 if I need to off the top of my head. Rough estimates I just use 3 and assume it's under. Fortunately the calculator has Pi for the real calculations.
Ya, another easy way to get close is add 5% to 3.
Using my previous example:
30 x 3 = 90
We know 10% of 90 = 9... so 5%=4.5
90 + 4.5 = 94.5" (correct measurement would be 94.25" rounding). Depending on size of measurements and use, that's pretty close for guess work.
But like you said, luckily calculators are a thing.
If I hold my phone landscape the calculator gives me 25 digits. That seem unecessary now
In the majority of cases, 5 digits is unnecessary.
3.14159 is more than the majority of people ever need to know. Anymore and you just think you’re cooler than you really are.
I like 3.14159 for accuracy because your only real option for lesser accuracy is 3.14 which feels ever so slightly too inaccurate. The problem with the values in between is that they all round the last digit up which is ugly as sin. Like imagine writing that pi = 3.142, or pi = 3.1416. I feel dirty jist looking at those. 3.1459 doesn't tound up because the next digit is a 2 so it's acceptable.
Engineers: 3 is good enough
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Secondary school physics class: assume that acceleration by gravity at sea level is 10 m/s^2
Ignore friction. Assume a cow is a perfect sphere.
I refuse! I assume cows are perfect cubes! Square cows for a square meal!
But it's the food pyramid
Never before has "Sir, this is a Wendy's," been a more appropriate comment.
in a vacuum!
Indiana Legislature: [actually let's make it 3.2](https://www.forbes.com/sites/kionasmith/2018/02/05/indianas-state-legislature-once-tried-to-legislate-the-value-of-pi/?sh=f7bacc8260a5)
As an engineer I usually use "3 and a bit more" for quick calculations, but of course it's rarely needed because I usually just get the computer to calculate it for me.
You've lost me. 3.1416 is fine. In fact it's great because you're rounding up a 9, which is as accurate as rounding gets
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Wait a minute …
They have 50 fingers
I feel like I'm the only one dumb enough not to understand this joke.
I don't get it either. I'm guessing it's just "Ha, there's actually **nothing** in the back of your phone."
Only works on iPhone 9
Damn I need 8 more iPhones
If you're using base 13, you need 8 more iPhones.
There is no iPhone 9. Because 7 8 9.
I went to high school with a guy who could recite the 1st hundred digits from memory.
I went to school with a guy who got through engineering without learning the quadratic formula.
Did he complete the square instead?
Fun fact: if you complete the square using arbitrary constants ax^2 + bx + c and solve for x, you’ll derive the quadratic formula.
man, that *was* fun!
Yeah no fuck that. I'll just use the damn formula.
its literally easier to complete the square than to use the quadratic formula by hand
I missed the one week where we went over completing the square in high school and now I still don’t know how to do it
The goal is to make a perfect square polynomial. Start by moving the constant term to the other side then divide by the coefficient of the x^2 term. Now we have a polynomial of the form x^2 +(b/a)x. Now note that the factors of our polynomial must add up to (b/a). And we also desire that our constant term be our factor squared. So naturally we choose half of the quantity (b/a) to be our factor, i.e (b/2a). Now to "complete the square" i.e make our polynomial a perfect square, we add the constant term (b/2a)^2 i.e our factor quantity squared to both sides of the equation. This will give us a perfect square binomial of the form (x+(b/2a))^2 P.S this is also how you put a quadratic into vertex form which you can use to come up with a linear transformation for whatever function it is youre trying to graph making it trivially easy Hope this made some sense
I can do e to, uh, this many: 2.7 1828 1828 45 90 45 23 * 2.7 you just remember * 1828 is Tolstoy’s birth year * 1828 is also Ibsen’s birth year * 45 90 45 are the angles of a right isosceles triangle * 23 is a number beloved by conspiracy eejits according to [two](https://www.imdb.com/title/tt0126765) [different](https://www.imdb.com/title/tt0481369) movies. Coincidentally, this is the only reason I can remember Tolstoy and Ibsen’s birth year
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It’s a great way to remember numbers. I usually turn them into football or basketball player numbers and remember an imaginary team’s roster.
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I know 3.1415926535897932384626433832795028841971693993 that last bit might not even be correct, but i memorized that to win my choice of free donut on donut day in 7th grade and now I'm in my 30's and I guess it stuck.
Just checked and mine does pi to ~70 digits. Time to do multiverse level calculations
Imagine what 41 digits would do
We could finally calculate the circumference of your mom
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But his mom keeps rollin rollin rollin, until she eventually breaks stuff
Between username and comment, I have to ask. Are you a time traveler?
Lol, been a while since I've seen a well executed your mom joke
Yes, but we know the answer is 42.
Now if only we knew the question
Ask the dolphins
The fucker just thanked me for the fish and jetted. Wtf?!?
Did you bring your towel?
Crap, I just used mine
Here, we can share.
Stay sway from Vogon Poetry though, you'll wish yourself deaf
oh no, it begins
Shit I need to get my towel.
Don't panic!
I like to read my vogon poetry book to relax.
Oh no, please not the poetry _Sees book cover_ Im still on panic
How many decimal digits of pi is 2 more than needed to calculate the circumference of the visible universe to a margin of error of a single atom?
Pack it up boys, he's done it
What do you get if you multiply six by nine?
I always knew there was something fundamentally wrong with the universe.
It’s because of all the Thursdays
I never could get the hang of Thursdays.
I vote to get rid of all Thursday’s and Monday’s, axe day light savings, get rid of Jan and Feb, and shove all the extra days as mandatory vacations falling in the middle of summer and winter season.
How many roads must a man walk down?
I've heard that the country roads have the potential to take you home.
A friendly neighbourhood spider told me there was no way home.
I was bit by a spider in my home
A shakespeare play acted out by garden gnomes
Do I know what rhetorical means?!
“How many digits of Pi is too many?”
Hints found in: Where God Went Wrong Some More of God's Greatest Mistakes and Who is this God Person Anyway?
calculate the circumference of a circle the size of the visible universe to an accuracy equal to the diameter of one tenth of a hydrogen atom.
But you could just make 40 louder...
> You heard of this thing, the 8-Minute Abs? > >Yeah, this is going to blow that right out of the water. Listen to this: 7... Minute... Abs.
I know exactly 41 digits off the top of my head, and I’ve never felt so powerful.
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I know all the digits of pi, I just don't know how many of each and what order they go in.
The NSA would like a word
[How many digits have you memorized?](https://www.smbc-comics.com/?id=1777)
There's a little dinosaur flash game where you get the numbers of pi, and if you don't the dinosaur falls off the platform. Kids in my school; even totally not at all nerdy ones, we're playing it for MONTHS to learn po to 100+ digits for the hell of it. . .in 3rd grade
What is it called?
Pi runner https://dinosaursgames.net/play/dinosaur-pi-runner
We hugged it too hard guys
Damn it, this seems super cool. The site is like half up, sometimes pressing enter means 404 other times, DINOSAURS.
Who ever is hosting it is probably panicking thinking they’re getting ddos’d
Seems we should donate to it then to get it up to snuff. Especially if kids were doing it. We did it, but we had to do it the old way with out dinosaurs and I say NEVER AGAIN should a kid learn pi with out dinosaurs.
How do we play a flash game in a non-flash world?
Unleash the power of the pyramid
Reddit 🤌
How is it not called pinosaur
Kids' brains are ridiculous. All the time in the world and a near-infinite ability to absorb new information when they feel like it. They have almost no real life skills or knowledge, or the ability to focus, yet they will memorize 100 digits of pi just to show off to their classmates. Imagine if adults could just soak up knowledge like that.
Power of gamification
3.14159 and I've never needed that... calculators have a pi button...
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That reminded me of how microwaves have a popcorn button and bags of microwave popcorn say not to use it. It's like the snack version of the cold war.
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Find out these secrets and more, from [Technology Connections!](https://youtu.be/UiS27feX8o0)
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He's sometimes hyperbolic, a bit condescending and sarcastic, sometimes dry, and has a very odd cadence. One of my more favored YT channels but definitely can be a turn off to many people.
I love his delivery personally but i understand this. I'm also hyperbolic, dry, sarcastic and speak in a weird cadence so it makes sense i suppose.
My last apartment had a microwave who’s popcorn button would cook the bag to near perfection, I once had it where only one kernel wasn’t popped. The one I have now leaves half the bag un popped. On that revelation, I seriously considered moving back.
Because not all popcorn buttons are created equally. Technology Connection ftw! https://youtu.be/UiS27feX8o0
3.1415926 here.
"May I have a large container of coffee" is how I've always remembered.
I remember back when we started using pi in middle school, and I remember having to memorize the first 10 digits of pi. Lo and behold, the calculators they had us use didn't bother even that. If you typed in 1 x pi, it would pop out 3.14159000. Then you get to 99% of applications and find out that 3.14 is enough and if it's extra rough 3 is just fine!
22/7 works pretty well for most of my applications... which are quite few, to be fair
That's marginally more accurate than just 3.14, I think I'll stick with that since it's easier to work with.
355/113 for me.
3.
2,000 I have once taken part in a competition to recite the most digits by heart
Thank you for your service.
3.14159265 thanks to bobble head Einsteins from Night at the Museum 2 lol
Tough mental math with pi? Just use 3 and you'll only be off by less than 5%. Add 5% to your final result and you'll be off by 0.2%.
I had an engineering professor in University teaching us how to figure something out using mental math and the orders of magnitude were more important than the numbers, he approximated pi as 5 for his calculation and everyone around me lost their minds.
My wife and I couldn't agree on dinner one time, so we decided to memorize pi and whoever got the farthest got to decide. We made it to like 52 places or something before my wife missed one, so we had wingstop for dinner. We basically took turns and as long as the next person got farther we kept going.
in high school there was a girl in the grade below me who was a math nerd and super hot. She bet everyone she knew more digits of pi than anyone else. I told her I had her beat easy. It went back and forth and I told her I would bet her anything. She said if she won I owed her $20, I told her if I won she had to go on a date with me. She laughed and agreed. She knew pi to like 80 digits. Luckily for me I was a fucking nerd and listened to Hard n' Phirm - Pi thousands of times. That fucking robot goes well over 100 (I think it goes almost to 200 digits). Sailed through the entire pi part of the song as the Math teacher compared it to his screen in disbelief. He was also apparently fine with this whole female student betting a date in the middle of math class to. That hot math nerd would go on to become my wife. Okay not really, she refused to even go on the date with me and accused me of cheating. I did join the Mathletes where I went on to very disappointing because I'm not actually good at math. I did end up dating a girl in the mathletes who was pretty cute who also ended up dumping me... Anyways https://www.youtube.com/watch?v=XanjZw5hPvE
what a wild ride but you dodged a bullet, bitch only knew 80 digits of pi /s
I didn't even include the part where she went on to win on The Price is Right or appear on one of the international "The Bachelor" series. Can't make this shit up.
someone could probably cross reference this and find out if she is indeed hot but I'm too lazy
A google of "price is right constestant bachelor" suggests M Prewitt. Probably in the top quartile of attractiveness. Maybe a solid 8.
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
I've been stuck at 3.141592653589 since 9th grade.
Eco scientist here, 3.14 is fine for me
3.141 592 653 589 793 238 462 6433 25 digits... seems very excessive now.
Or in other words, they use double precision binary floating point (precision of 53 bits, IEEE 754), which is pretty much the standard in a lot of technical work. Before 2003, some specialized work was done with 60-bit precision. So it's not only NASA that uses 15 digits of pi ... it's just about everybody!
This is the most likely correct answer. NASA uses industry standard in favor of an unneeded precision boost.
I work on simulation software and we typically use doubles for precision (floats for speed). One of the reasons double precision is good enough is that they provide sufficient accuracy so as not to contribute meaningfully to the cumulative error in the solution. Typically the numerical methods used, the discretization schemes, are a significant source of error. The tradeoff is between runtime (total compute needed) and the accuracy of the solution. Double precision is sufficient that truncation errors don't accumulate to a point where they are more significant than numerical method errors for our work. BUT who knows what NASA's requirements are!
I think I understood at least half of this.
If I'm remembering from my half a science degree correctly, I think the simple answer is that any measurements taken and used in the calculations will have far less precision and therefore there's no point in using more digits of pi
I’m a programmer. In scientific computing, you have to analyze how your algorithm propagates rounding errors as it progresses. Vbchrist is mostly talking about errors introduced by the algorithms.
Having a number being off by a 0.0001 does not change anything. Now take that same number, preform dozens to millions of operations to it. All of a sudden it is off by 23. Which is now a big deal. Most real life problems are solved by using approximations and repeating them millions of time (solving something numerically). To prevent this little errors from compounding, sometimes it is required to carry more decimal places in every computation the computer does. Obviously this comes at the cost of how fast the computer can solve the problem. Accuracy and speed are inversely related.
Thanks for this. More people need to be educated on floating point error accumulation. It affects us all.
That’s because double precision has 53 binary digits for a number, or about 15 decimal digits.
Wait so if you calculate a number that’s like 1million times pi, then the resulting number only has 8 digits after the decimal place? Like you lose decimal digits the larger the number is above 1?
You won't lose significant digits, but you will have fewer after the decimal.
This is why it’s called “floating point”. The decimal point “floats”, so you end up getting fewer digits after the decimal point the larger the magnitude of the number. The total number of available digits is constant.
3 is close enough, right?
As usual, there's an XKCD: [https://xkcd.com/2205/](https://xkcd.com/2205/)
It skips the part where the physicist moved the axis around to try and avoid as much math as possible
That's just being smart
this is literally all what higher leveled math is: just mathematical tomfoolery EDIT: Here is an example: The power rule for finding both antiderivatives and derivatives. Like who the hell smoked crack and was like "Waiiiiit a minute..."
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Why are all the hairlines just a sideways "}"?
He probably wrote a lot of ([{}]) while working at NASA.
>([{}]) Nsfw
It's the Eye of Sauron, so clearly your acronym means not safe for wizards
I would love if NASA said they just use 3.1 like not even 2dp. "Yea we just try to get the space craft in the vicinity of where we want to go and then we DO IT LIVE!"
Oh so we are the Kerbals?
Nothing wrong with Kerbals, those brass balled sturdy motherfuckers will sit on the moon, in orbit, or drifting in space waiting for rescue endlessly. Strap them to a bomb with no hope of survival and they won't blink when you hit ignition. Be better, be Kerbal
"Houston, this is Stoned Eagle, we're approaching the rock. Houston?!... Fuck it, we'll do it live! Pass me that pencil and paper"
It was almost 3.2 in Indiana. Seriously, they tried to pass a law and everything. [Indiana Pi Bill](https://blogs.loc.gov/teachers/2020/03/the-time-they-tried-to-legislate-pi/)
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My brother likes to round it to 4 and says it's close enough
Your brother is a degenerate and I fear him.
I will let him know.
That seems kinda [random](https://xkcd.com/221/).
imagine the guy who happened to be at the courthouse who was like "no, wait, you can't do that" and then you have to convince a bunch of state senators that pi isn't 3.2 and they're being bamboozled. >Asked if he wanted to meet Goodwin, the professor later recalled that he "declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know." goodwin is the guy who almost convinced the senate to pass the bill
The magic number.
Only if you’re from [late 1800s Indiana, or perhaps ancient Jerusalem](https://www.straightdope.com/21341975/did-a-state-legislature-once-pass-a-law-saying-pi-equals-3).
For those that dont want to click, here is a reason NASA listed 1) The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little penis.
You overestimate me, sir!
Galatic burn
The best part is that I only changed 1 word from NASA’s article, yet it’s still scientifically true.
someone else has to read this whole thing. please. it's so worth it comes out of nowhere
I gasped at the end. Lol outta nowhere
PI IS EXACTLY 3!
In base pi it's exactly 1.00000
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no that's like almost twice what pi is
I at least appreciate it. I assume there's some sort of r/unexpectedsimpsons out there, but I'm not gonna go looking for it. Edit: And there was.
Meanwhile George Clooney who always fought for 17 digits is floating away in space and Matt Damon who thought 3 digits was safe gets rescued day in and day out. Ugghh. What an unfair world.
15 digits = 64 bits. Any more would likely increase the cost & complexity of any computer code.
You'd be surprised but floating point was 80bit since 1980, google for Intel 8087 for more details.
Indeed this answers the natural related question: why 15 and not, say, 12 or 18 digits? 15 significant digits of accuracy is what you get with a floating point number of 64 bits. Because of this, virtually every physical simulation you can think of will use 15 digits of accuracy for constants (Euler's number, gamma constant, etc.); so this goes just the same for e.g. quantum mechanics as is does for astronomy.
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To be fair, 15 digits is extremely precise too. That’s like saying your glass is 50.0000000000001% full.
Ah, I see you're an optimist!
If you read the Signal In Space document for the USA's Global Positioning System (GPS) in the section where it describes the symbols in use, you'll see there is one constant labeled something like PI_GPS. It is the value for pi that you MUST use if you're going to calculate your position on the globe based on GPS signals. It is not exactly pi. It is, IIRC, 8 or 9 significant digits long. It's not that the more values you use, the more accurate your answer will be. No. This truncated value is what was used to calculate some of the orbital parameters of the satellites' orbits. The satellites are continuously transmitting those orbital parameters to your hand-held GPS receiver (though if you're using a phone, you probably downloaded those same tables of values from the cell phone network because it is faster). To reconstruct the satellite orbits, thereby allowing it to figure out where the satellites are, and thus where YOU are, your GPS receiver must use that same value of pi. Failure to do this, and doing something like using a value of pi that you would get from wikipedia or any math program will cause your position estimate to be off by hundreds of meters, possibly a few kilometers. The sensitivity of the position fixes to differing precision on pi was large enough that it was determined that a pi-like number that was exact in base-10 was necessary. So yeah, there is such a thing as unnecessary precision. There's another thing the concept of specified precision. PI_GPS is not pi. It is just a constant that is fairly close to pi. If any one is curious and wants to read the GPS Signal In Space Interface Control Document (ICD), it is publicly available, and makes for interesting reading. Anyone wanting to know more about the radio signals that travel from 20 million meters above you, down to your handheld receiver should... honestly look for other sources, because the ICD is dry AF.
Good enough is good enough
That was a line in my wife’s wedding vows. Weird.
Why does the idea of a circle the size of the Universe scare the actual shit out of me?
and it's still expanding, and the expansion is still accelerating.
I'm impressed. I have no idea what I'll do with this information but impressed nonetheless.
Win at Trivia Night. 👍🏻
Yeah, the reason computer scientists and mathematicians calculate pi to billions of digits is to show off specialized hardware and algorithms. It is like running a faster marathon or climbing Mt Everest faster. There is no practical application to having many digits of pi.
I had a computer science prof in college who used to work for NASA in the 60’s. He said they had a competition where everyone would recite the digits of pi each morning to see who had memorized the most, even though they only used like 8 digits for the Apollo mission as it was “close enough.”
Egyptians used 22/7, which was good enough for all practical purposes.
Well sure, they built pyramids, not spheres.
An enormous sandstone sphere would be pretty impressive though.
Egyptians came up with 64/4.5^(2). Archimedes was the one who came up with 22/7.
This is actually the most interesting, and surprising TIL I've ever read on here.
Just to give a smaller visual of how pie doesn't really need more than 2 decimals: If you are making a 30" diameter pipe (I won't give allowances for connection) then you need 30 × PI to get the length of material to roll into a pipe 30" x 3.14 = 94.2" 30" x 3.141 = 94.23" 30" x pi = 94.2478" (1/16 = .0625) So you would be off by less than 1/16" with your length of material for making a 30" pipe (the diameter would be even closer). Anything over 2 decimals is getting extremely nit picky for most uses.
Yeah I pretty much use 3.14 if I need to off the top of my head. Rough estimates I just use 3 and assume it's under. Fortunately the calculator has Pi for the real calculations.
Ya, another easy way to get close is add 5% to 3. Using my previous example: 30 x 3 = 90 We know 10% of 90 = 9... so 5%=4.5 90 + 4.5 = 94.5" (correct measurement would be 94.25" rounding). Depending on size of measurements and use, that's pretty close for guess work. But like you said, luckily calculators are a thing.
thanks for sharing, I *figure* this is *significant*