6 ms·

π = 3 (sometimes) for Nobel laureate

105 points by starpilot 16y ago

happy4crazy 16y ago
Ha, in one of my physics classes the professor actually set pi = 1 :)
goalieca 16y ago
This guy sounds like every microelectronics prof ever. :) I took that to heart when doing the exams and it make the impossible possible.
- slackerIII 16y ago
  I really enjoyed it when my EE professors would simply erase components of a circuit diagram if they didn't matter and they made things complicated. I think that had an impact on my approach to solving problems.
  - ableal 16y ago
    Another trick of the trade is working back from the desired output by stages. For example, for an amplifier delivering 200 W to loudspeakers (or 1 kW to an antenna, or ...), first design the final stage, then work back from that adding the stages needed until the range is OK for the input signal you have.
- wging 16y ago
  My favorite one of these comes from physics. Simple harmonic motion impossible to deal with? Voila, assume |sin(x) - x| is small and just deal with x instead of sin(x)--magic!
juiceandjuice 16y ago
Every russian professor I had loved gaussian units. I learned to love them too. Everything is simpler when you don't have 3-5 constants staring you in the face.
Jabbles 16y ago
Hmm, whilst it's true physicists often simplify equations to really understand the problem, I can't think of a variable in quantum mechanics we "don't know to within 2 orders of magnitude". Especially one called alpha, which usually denotes the fine structure constant, which we know to better than 1 in a billion... Anyone have some thoughts on what it could be, if true? http://en.wikipedia.org/wiki/Fine-structure_constant http://en.wikipedia.org/wiki/Fine-structure_constant
- jessriedel 16y ago
  > I can't think of a variable in quantum mechanics we "don't know to within 2 orders of magnitude". Maybe the neutrino masses differences? In my intro QM class, we did a problem where we calculated the distance it took for one neutrino flavor to mix into another, which depends on the mass differences. You wouldn't want to take a square root of eV, though. Or it could be it's one of the CKM angles. The latter are known to 1 part in 10^4, but only because of the relatively recent BaBar and BELLE experiments. Maybe back when this guy was an undergrad they only know them to 1 part in 100. Seems kinda advanced for 3rd semester of QM...
- tygorius 16y ago
  Two aspects spring to mind. First, we don't know how long ago this course was, so it's quite possible some of the story is either dated or a slightly misremembered anecdote for a physicist who was brought up with slide rules for his calculations. Second, the quote specifies "experimentally", which implies measurements limited to two orders of magnitude, i.e., measured vs theoretical. Alas, while I have a few slipsticks in the closet, I am not now nor have I ever been a physicist, so I could be totally wrong on this.
- harshpotatoes 16y ago
  You're overthinking this. Yes, in principle we do known the fine structure constant to something like 9 orders of magnitude both experimentally and theoretically. However, when would you use the pi = 3 approximation? Certainly not when you're in front of a computer, or if you were preparing some experimental results for publication. But, if you're in the lab and need to quickly make some calculations, or just to see if something is feasible and worth spending more time on, pi = 3 isn't so bad. Example, measuring the fine structure. Sure, you can predict where these energy levels are supposed to be to probably whatever our error on knowing the mass of an electron is. And because you know the fine structure so precisely, you should be able to make a very accurate prediction on where that is. However, throw most of those digits out the door, because a lot will be hidden behind doppler broadening. So when you make your measurement in your fabry perot etalon, you'll probably make a precise measurement http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_Fringes.png http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_F... but how accurately can you really measure the position of those fringes? Sure, free spectral range probably lets you get down to about MHz region or so, but the doppler broadened linewidth is probably an order larger than that. Which brings us back to, you've got these experimental errors, why care about 9 digits of precision if you just want a quick and dirty calculation to get things set up? Anyways, that's all he's trying to say. In most experiments, there will be some sort of experimental error hurting you. Be sloppy in the beginning just to get a feel for things.
clarkevans 16y ago
Any person with a marketing degree will tell you this is false. Try to bill for a circular billboard (say a circular podium at a conference booth) where ~4.7% of the surface lacks proper advertisements or necessary background color.
deleted 16y ago
[deleted]
dhimes 16y ago
Pi ~ 3, but we also often need Pi^2, which is better approximated as 10. (I actually got into an argument about rounding Pi^2 to 10 once with a person who liked to round Pi to 3 ...)
- bdhe 16y ago
  I remember using Pi^2 to be approximately g (the acceleration due to gravity near the earth's surface). This comes in real handy when simplifying the time period of a pendulum.
  - dhimes 16y ago
    Yep- and rounding g to 10 m/s^2 when there's no pi involved- so you can actually talk conversationally about free-fall because you can then do the math in your head.
- madcaptenor 16y ago
  Pi is about 3. Pi^2 is about 10. But better than both of these approximations is Pi^2 + Pi = 13, which gives Pi = (-1 + sqrt(53))/2 = 3.1400... (It's too bad that the combination Pi^2 + Pi occurs basically never.)
Fester 16y ago
I got exactly the same lesson in almost similar situation, but from a guy who was not even close to (someone who is close to) a Nobel's prize. He did a sum of a problem from the test using a small constants reference book and his head. Despite the numerous simplifications in the calculation, error of his result was less then 5%.
splat 16y ago
It's a little unrelated, but if you ever need to know the number of seconds in a year, it's pi x 10^7 to within .5%.
- dmnd 16y ago
  Proof for the curious: http://www.google.com/search?q=number+of+seconds+in+a+year+divided+by+(pi+*+10^7) http://www.google.com/search?q=number+of+seconds+in+a+year+d...
  - omh 16y ago
    I understand what you did, but the mathematician in me cringed at the word "proof" in that comment.
    - itsnotvalid 16y ago
      May be the word "fact" would be better to describe these kind of numbers.
    - jberryman 16y ago
      proof by googlization
    - guelo 16y ago
      That looked like a mathematically rigorous proof to me. What was wrong with it?
    - likpok 16y ago
      Proof by construction is perfectly valid, if usually too difficult to be useful.
- ez77 16y ago
  Or, as stated in Bertley's "Programming Pearls": Pi seconds is a nanocentury.
guylhem 16y ago
I will never forget an high school assignment in physics in France, where we were asked to calculate how a wheel of a given diameters would put marks to the road if it had a pen attached at a given position. Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. So I started by "let's define pi=3" I got a bad grade on that one, even after I protested that the answer was within the required specifications, so afterwards as a nag, I was always over-precise with her assignments - like always included electron mass in nucleus calculations :-)
- lukeschlather 16y ago
  >Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. In English, calculus and calculation are two different things. And there are a number of grammatical errors in that sentence that make the meaning unclear. I'm noting this because if the teacher allowed you to do simpler calculus so long as you maintained an error margin of 10%, that's different from allowing you to do simpler calculations provided you keep an error margin of 10%. Calculus is specifically the branch of mathematics involving limits, functions, derivatives, and integrals, and from the English it sounds like she, if we are being perfectly pedantic, was giving you the option do do approximations with your integrals and derivatives, not with any value you like.
  - kwantam 16y ago
    You're being pedantic in English in response to an exchange that presumably happened in French. :)
  - dfranke 16y ago
    Newton's calculus is just one example of a calculus. A calculus is any set of mechanical rules for manipulating mathematical symbols. Calculation is the process of applying those rules. Cf. the lambda calculus. The branch of mathematics involving limits, functions, derivatives, and integrals is analysis.
    - 16y ago
zipdog 16y ago
That's rather close to a smbc comic: http://www.smbc-comics.com/index.php?db=comics&id=1777#comic http://www.smbc-comics.com/index.php?db=comics&id=1777#c... (it was previously on Hacker News: http://news.ycombinator.com/item?id=1093703 http://news.ycombinator.com/item?id=1093703)
FaceKicker 16y ago
Off topic, but why is the "pi" character in most common fonts so poorly designed? It always seems to have a straight line at the top rather than a tilde-like stroke and it confuses me just about every time.
- syncsynchalt 16y ago
  I had the same problem, I thought the author mistakenly used ∏ but I see in my browser tab that it's correctly lowercase.
  - JBrone 16y ago
    I read n = 3. I thought I was coming into a discreet calculus thread. Then i find it's continuous and got upset. Then I find that it's not even american calculus which makes me even more upset. I'm going to have to hammer out a few combinatoric problems regarding the probability of picking a McNuggets box with TWO boot-shaped nugs just to get my credibility back. /silly
tybris 16y ago
How was it funny? It seems like a sound reasoning, depending on whatever alpha represents.
- JBrone 16y ago
  It's funny because the students thought he was being cheeky, when in fact he was making a logical leap that few individuals would EVER make, much less in a random junior level physics course. He basically Nerd-burned them, and that is something I can get behind.
ciupicri 16y ago
As my programming teacher used to say when talking about floating numbers and their errors, π is 5 in agriculture and 3.14159 in civil engineering.

105 points by starpilot 16y ago

Ha, in one of my physics classes the professor actually set pi = 1 :)

This guy sounds like every microelectronics prof ever. :) I took that to heart when doing the exams and it make the impossible possible.

slackerIII 16y ago
I really enjoyed it when my EE professors would simply erase components of a circuit diagram if they didn't matter and they made things complicated. I think that had an impact on my approach to solving problems.
- ableal 16y ago
  Another trick of the trade is working back from the desired output by stages. For example, for an amplifier delivering 200 W to loudspeakers (or 1 kW to an antenna, or ...), first design the final stage, then work back from that adding the stages needed until the range is OK for the input signal you have.
wging 16y ago
My favorite one of these comes from physics. Simple harmonic motion impossible to deal with? Voila, assume |sin(x) - x| is small and just deal with x instead of sin(x)--magic!

juiceandjuice 16y ago

Every russian professor I had loved gaussian units. I learned to love them too. Everything is simpler when you don't have 3-5 constants staring you in the face.

Jabbles 16y ago

Hmm, whilst it's true physicists often simplify equations to really understand the problem, I can't think of a variable in quantum mechanics we "don't know to within 2 orders of magnitude". Especially one called alpha, which usually denotes the fine structure constant, which we know to better than 1 in a billion... Anyone have some thoughts on what it could be, if true? http://en.wikipedia.org/wiki/Fine-structure_constant http://en.wikipedia.org/wiki/Fine-structure_constant

jessriedel 16y ago
> I can't think of a variable in quantum mechanics we "don't know to within 2 orders of magnitude". Maybe the neutrino masses differences? In my intro QM class, we did a problem where we calculated the distance it took for one neutrino flavor to mix into another, which depends on the mass differences. You wouldn't want to take a square root of eV, though. Or it could be it's one of the CKM angles. The latter are known to 1 part in 10^4, but only because of the relatively recent BaBar and BELLE experiments. Maybe back when this guy was an undergrad they only know them to 1 part in 100. Seems kinda advanced for 3rd semester of QM...
tygorius 16y ago
Two aspects spring to mind. First, we don't know how long ago this course was, so it's quite possible some of the story is either dated or a slightly misremembered anecdote for a physicist who was brought up with slide rules for his calculations. Second, the quote specifies "experimentally", which implies measurements limited to two orders of magnitude, i.e., measured vs theoretical. Alas, while I have a few slipsticks in the closet, I am not now nor have I ever been a physicist, so I could be totally wrong on this.
harshpotatoes 16y ago
You're overthinking this. Yes, in principle we do known the fine structure constant to something like 9 orders of magnitude both experimentally and theoretically. However, when would you use the pi = 3 approximation? Certainly not when you're in front of a computer, or if you were preparing some experimental results for publication. But, if you're in the lab and need to quickly make some calculations, or just to see if something is feasible and worth spending more time on, pi = 3 isn't so bad. Example, measuring the fine structure. Sure, you can predict where these energy levels are supposed to be to probably whatever our error on knowing the mass of an electron is. And because you know the fine structure so precisely, you should be able to make a very accurate prediction on where that is. However, throw most of those digits out the door, because a lot will be hidden behind doppler broadening. So when you make your measurement in your fabry perot etalon, you'll probably make a precise measurement http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_Fringes.png http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_F... but how accurately can you really measure the position of those fringes? Sure, free spectral range probably lets you get down to about MHz region or so, but the doppler broadened linewidth is probably an order larger than that. Which brings us back to, you've got these experimental errors, why care about 9 digits of precision if you just want a quick and dirty calculation to get things set up? Anyways, that's all he's trying to say. In most experiments, there will be some sort of experimental error hurting you. Be sloppy in the beginning just to get a feel for things.

clarkevans 16y ago

Any person with a marketing degree will tell you this is false. Try to bill for a circular billboard (say a circular podium at a conference booth) where ~4.7% of the surface lacks proper advertisements or necessary background color.

deleted 16y ago

[deleted]

dhimes 16y ago

Pi ~ 3, but we also often need Pi^2, which is better approximated as 10. (I actually got into an argument about rounding Pi^2 to 10 once with a person who liked to round Pi to 3 ...)

bdhe 16y ago
I remember using Pi^2 to be approximately g (the acceleration due to gravity near the earth's surface). This comes in real handy when simplifying the time period of a pendulum.
- dhimes 16y ago
  Yep- and rounding g to 10 m/s^2 when there's no pi involved- so you can actually talk conversationally about free-fall because you can then do the math in your head.
madcaptenor 16y ago
Pi is about 3. Pi^2 is about 10. But better than both of these approximations is Pi^2 + Pi = 13, which gives Pi = (-1 + sqrt(53))/2 = 3.1400... (It's too bad that the combination Pi^2 + Pi occurs basically never.)

Fester 16y ago

I got exactly the same lesson in almost similar situation, but from a guy who was not even close to (someone who is close to) a Nobel's prize. He did a sum of a problem from the test using a small constants reference book and his head. Despite the numerous simplifications in the calculation, error of his result was less then 5%.

splat 16y ago

It's a little unrelated, but if you ever need to know the number of seconds in a year, it's pi x 10^7 to within .5%.

dmnd 16y ago
Proof for the curious: http://www.google.com/search?q=number+of+seconds+in+a+year+divided+by+(pi+*+10^7) http://www.google.com/search?q=number+of+seconds+in+a+year+d...
- omh 16y ago
  I understand what you did, but the mathematician in me cringed at the word "proof" in that comment.
  - itsnotvalid 16y ago
    May be the word "fact" would be better to describe these kind of numbers.
  - jberryman 16y ago
    proof by googlization
  - guelo 16y ago
    That looked like a mathematically rigorous proof to me. What was wrong with it?
  - likpok 16y ago
    Proof by construction is perfectly valid, if usually too difficult to be useful.
ez77 16y ago
Or, as stated in Bertley's "Programming Pearls": Pi seconds is a nanocentury.

guylhem 16y ago

I will never forget an high school assignment in physics in France, where we were asked to calculate how a wheel of a given diameters would put marks to the road if it had a pen attached at a given position. Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. So I started by "let's define pi=3" I got a bad grade on that one, even after I protested that the answer was within the required specifications, so afterwards as a nag, I was always over-precise with her assignments - like always included electron mass in nucleus calculations :-)

lukeschlather 16y ago
>Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. In English, calculus and calculation are two different things. And there are a number of grammatical errors in that sentence that make the meaning unclear. I'm noting this because if the teacher allowed you to do simpler calculus so long as you maintained an error margin of 10%, that's different from allowing you to do simpler calculations provided you keep an error margin of 10%. Calculus is specifically the branch of mathematics involving limits, functions, derivatives, and integrals, and from the English it sounds like she, if we are being perfectly pedantic, was giving you the option do do approximations with your integrals and derivatives, not with any value you like.
- kwantam 16y ago
  You're being pedantic in English in response to an exchange that presumably happened in French. :)
- dfranke 16y ago
  Newton's calculus is just one example of a calculus. A calculus is any set of mechanical rules for manipulating mathematical symbols. Calculation is the process of applying those rules. Cf. the lambda calculus. The branch of mathematics involving limits, functions, derivatives, and integrals is analysis.
  - 16y ago

zipdog 16y ago

That's rather close to a smbc comic: http://www.smbc-comics.com/index.php?db=comics&id=1777#comic http://www.smbc-comics.com/index.php?db=comics&id=1777#c... (it was previously on Hacker News: http://news.ycombinator.com/item?id=1093703 http://news.ycombinator.com/item?id=1093703)

FaceKicker 16y ago

Off topic, but why is the "pi" character in most common fonts so poorly designed? It always seems to have a straight line at the top rather than a tilde-like stroke and it confuses me just about every time.

syncsynchalt 16y ago
I had the same problem, I thought the author mistakenly used ∏ but I see in my browser tab that it's correctly lowercase.
- JBrone 16y ago
  I read n = 3. I thought I was coming into a discreet calculus thread. Then i find it's continuous and got upset. Then I find that it's not even american calculus which makes me even more upset. I'm going to have to hammer out a few combinatoric problems regarding the probability of picking a McNuggets box with TWO boot-shaped nugs just to get my credibility back. /silly

tybris 16y ago

How was it funny? It seems like a sound reasoning, depending on whatever alpha represents.

JBrone 16y ago
It's funny because the students thought he was being cheeky, when in fact he was making a logical leap that few individuals would EVER make, much less in a random junior level physics course. He basically Nerd-burned them, and that is something I can get behind.

ciupicri 16y ago

As my programming teacher used to say when talking about floating numbers and their errors, π is 5 in agriculture and 3.14159 in civil engineering.