
π = 3 (sometimes) for Nobel laureate - starpilot
http://ask.metafilter.com/182210/Is-this-where-Im-supposed-to-use-the-phrase-selfappointed-defender-of-the-orthodoxy#2621825
======
guylhem
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
>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.

~~~
dfranke
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.

~~~
lukeschlather
>The branch of mathematics involving limits, functions, derivatives, and
integrals is analysis.

Everywhere I've studied, it's been referred to as simply calculus. Wikipedia
says the same. I did take a class called analysis of functions in high school
as an advanced track pre-calculus, but your definition really does not apply
in the States at any rate. Where did you hear Analysis used to specifically
apply to what we call calculus in the States?

<http://en.wikipedia.org/wiki/Analysis#Mathematics>

~~~
dfranke
My usage is that which is universally accepted in any university math
department. As a freshman in a math/science/engineering major, you take (or
finish after beginning in high school) three semesters of Calculus, always
referred to with a capital "C" to mean specifically Newton's calculus. Here
you learn to _calculate_ integrals and derivatives so that you can use them as
a tool. If you major in math, then as a junior or senior you will take
analysis. Here is where you _rigorously study_ integrals and derivatives. An
introductory analysis course typically begins by defining Cauchy sequences,
and then defining the real numbers as equivalence classes of Cauchy sequences
of rationals. Building on this foundation, you then construct the basic theory
of continuous functions, derivatives, and Riemann integrals. Finally, you use
this theory to prove that the transformation rules of Newton's calculus are
sound.

------
Jabbles
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>

~~~
harshpotatoes
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_F...](http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_Fringes.png)

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.

------
FaceKicker
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
I had the same problem, I thought the author mistakenly used ∏ but I see in my
browser tab that it's correctly lowercase.

~~~
JBrone
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

------
splat
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
Proof for the curious:
[http://www.google.com/search?q=number+of+seconds+in+a+year+d...](http://www.google.com/search?q=number+of+seconds+in+a+year+divided+by+\(pi+*+10^7\))

~~~
omh
I understand what you did, but the mathematician in me cringed at the word
"proof" in that comment.

~~~
guelo
That looked like a mathematically rigorous proof to me. What was wrong with
it?

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

~~~
slackerIII
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
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.

------
dhimes
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
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
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.

------
juiceandjuice
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.

------
zipdog
That's rather close to a smbc comic: [http://www.smbc-
comics.com/index.php?db=comics&id=1777#c...](http://www.smbc-
comics.com/index.php?db=comics&id=1777#comic)

(it was previously on Hacker News:
<http://news.ycombinator.com/item?id=1093703>)

------
ciupicri
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.

------
Fester
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%.

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

~~~
JBrone
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.

------
happy4crazy
Ha, in one of my physics classes the professor actually set pi = 1 :)

------
clarkevans
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.

