1047: "Approximations"

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Re: 1047: "Approximations"

RyanfaeScotland wrote:I notice Randall uses billions for the world population but millions for the US population. Why is he being dishonest?

Wait, what?

I was expecting one of the pi approximations but there were none.

Eshru

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Re: 1047: "Approximations"

Eshru wrote:
RyanfaeScotland wrote:I notice Randall uses billions for the world population but millions for the US population. Why is he being dishonest?

Wait, what?

I was expecting one of the pi approximations but there were none.

http://www.xkcd.com/558/

RyanfaeScotland

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Re: 1047: "Approximations"

\pi = \sqrt[3]{31}, true within 1 in 5000
obarey

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Re: 1047: "Approximations"

My dad always taught me it as: 10\pi Ms in a year. Yes, you could just say \pi \times 10^7, but the more straight-faced you say 'megaseconds', particularly while teaching, the more entertaining it becomes for you.
E'Bahn

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Re: 1047: "Approximations"

reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.
Noir_Desir

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Re: 1047: "Approximations"

http://mrob.com/

Awesome page for people interested in RIES
Apparently, 1 in 5 people in the world are Chinese. And there are 5 people in my family, so it must be one of them. It's either my mum or my dad. Or my older brother Colin. Or my younger brother Ho-Chan-Chu. But I think it's Colin -- Tim Vine

shashwat986

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Re: 1047: "Approximations"

Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.

How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.

Klear

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Re: 1047: "Approximations"

Tuinkabouter wrote:Even now you're too much of a mathematician to dare to say \pi \approx \sqrt{10}. kudos.

Oh, man, that was one of my favorite bits from high school physics, when the teacher (walking us through a new type of problem on the board) rhetorically asked as permission to treat pi^2 as 10, for ease of calculation... we were of course aghast (esp. since in practical terms we generally learned to leave pi in there, it usually comes out in the wash) but then we went to show it's a closer approximation than saying "g is 10", which we did all the damn time.
http://kisrael.com/ - quotes and links daily

kirkjerk

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Re: 1047: "Approximations"

Using several different calculators, I'm getting the Whitehouse Switchboard # as one digit off: .2024561414923965799[...] which works of you truncate but not if you round as would be expected. (The Whitehouse switchboard is 202-456-1414.) But then, I guess it is an approximation...

--SMQ

smq

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Re: 1047: "Approximations"

pi^2 is a pretty good approximation for g already
amod00

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Re: 1047: "Approximations"

Math is a beautiful and poetic language.
Math has elegant rules, like all languages.

To bend the rules and not break them is a skill, to be sure.

It must be very difficult inside his head. He can do that AND be normal?

Good Him!

How long do you think that takes? Can he sit down and blow through a thing like that from memory? In what? Ten minutes?

Or; Does he doggedly move from one system of measure to the next, until a circuit blows in his head?

A thing like that makes me wonder. I like watching people do that kind of work. Computers sure make it easier. Less entertaining for me, but, easier for the person doing the work.

What were Mathematicians like before the computer?

Just like, now. Not all were the same.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

Those that want to Know, Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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Re: 1047: "Approximations"

At least two of the "accurate to within" margins are lower than the uncertainty in the value estimated: the ocean's volume and the age of the universe.
OP Tipping

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Re: 1047: "Approximations"

mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

That's my favorite as well. It's good to better than 1 in 10^7, which makes it as good as perfect for very nearly all real world purposes. (For instance, in 1e-7 hours, an object moving at mach 2 covers less than ten inches.)
-- Joe
"[Some people don't believe in coincidence, but] I believe in coincidence. Coincidences happen every day. I just don't trust coincidence."
Elim Garak

jqavins

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Re: 1047: "Approximations"

smq wrote:Using several different calculators, I'm getting the Whitehouse Switchboard # as one digit off: .2024561414923965799[...] which works of you truncate but not if you round as would be expected. (The Whitehouse switchboard is 202-456-1414.) But then, I guess it is an approximation...

--SMQ

If you just keep dialing digits, only the first 10 will be used by the phone system, I believe.
tomsing

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Re: 1047: "Approximations"

THIS ep is why I read this comic. And come to this forum.

>sniff< it's BEAUTIFUL.
beav

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Re: 1047: "Approximations"

jqavins wrote:
mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

That's my favorite as well. It's good to better than 1 in 10^7, which makes it as good as perfect for very nearly all real world purposes. (For instance, in 1e-7 hours, an object moving at mach 2 covers less than ten inches.)
And so elegant, to boot. 2 1's, 2 3's, 2 5's. Write them in order, bisect and assemble the fraction, you'll never forget it.
Van wrote:Fireballs don't lie.

VectorZero

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Re: 1047: "Approximations"

This would make an excellent poster. I'd buy it in a heartbeat. They're just so elegant and cool!

deoxys9

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Re: 1047: "Approximations"

Shidoshi wrote:
Shidoshi wrote:The gas constant is expressed in J/gmol.K and not J/kgmol.K which would be the SI unit.

I've never seen the abbreviations "gmol" or "kgmol", but the SI units of the gas constant are Joules per mole Kelvin, and moles are defined as if they were based on grams instead of kg. Probably because the chemists threatened insurrection otherwise... grams are a much more convenient laboratory unit.

I've been recently through ChemEng and now they are starting to use "kilogram moles" and "gram moles", that way everything can be expressed in kg without much problem. Carbon12's molar mass is 12g/gmol or 12kg/kgmol (or even 12lb/lbmol if you swing that way). It's a somewhat new concept yeah, but it sure helps putting everything to SI and making less confusion.

The SI unit for "amount of substance" is the mole:
http://www.bipm.org/en/si/base_units/
"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12."

And the current Wikipedia article on the mole says:
"In the metric system, chemical engineers once used the kilogram-mole (noted kg-mol), which is defined as the number of entities in 12 kg of 12C, and often referred to the mole as the gram-mole (noted g-mol), when dealing with laboratory data.[17] However modern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units."
[Reference 17 is to an engineering text published (as its 6th Ed.) in 1996.]

So the kg-mol is 1. not new, and 2. not SI.

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Re: 1047: "Approximations"

bitwiseshiftleft wrote:Also, e^(pi * sqrt(163)) ~ 640320^3 + 744. But that one is famous. And was found by a method other than brute force.

Damn, you beat me to it.

I once had parking permit number 163 at work. One weekend, the hang tag somehow got lost from the driver's door pocket I had been keeping it in and I had to apply for a replacement. Although I asked for a re-issue of the same number on the grounds that the number was easy to remember (citing the near equality above), they couldn't give it to me.

da Doctah

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Re: 1047: "Approximations"

How could he miss the best approximation of all?

pi^2 = 9.8696
g = 9.78 to 9.82

That one is actually useful in basic physics, since the period of a small angle pendulum is:
T=2 pi sqrt(L/g) --> T = 2 sqrt(L)
Sinnombre

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Re: 1047: "Approximations"

My personal favorite, or at least the one I use with my math students, is
\pi \approx \sqrt[4]{\frac{2143}{22}}.
I found it by accident.
Spoiler:
Well actually, while playing with a calculator while on the toilet...
anchises868

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Re: 1047: "Approximations"

I had a problem with Jenny's constant until I realized that that was a minus sign in the exponent, not a "dot" for multiplication.
cburke

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Re: 1047: "Approximations"

alextrabec wrote:Randall wins again. P.S. You are all nerds fact checking a web comic. Great Job, make your professors proud! Also, your mom plus me makes a "That what she said joke" - Enjoy

Love the comics and nerds, keep it up bitches!

Or the comic could have been titled "Pedantry Test". You know who you are.

Have a safe day.

San Fran Sam

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Re: 1047: "Approximations"

mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

This fails for Jenny's constant.
top1214

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Re: 1047: "Approximations"

I'm loving this table. I spend a lot of time figuring out approximations (mostly for equivalence functions, like converting Rockwell Hardness-C to Brinell Hardness Number: bhn = 89.75 + 28.5125*hrc - 0.1905*hrc**2 + 0.00315*hrc**3, coming soon to a CPAN module near you), but Randall's are just awesome.

The error in the sqrt(2) formula bothers me a lot .. I've edited my copy of the image so the "-" is "+", but the edit looks bad. I don't suppose Randall ever reads these forums and might post a corrected image? That would be wonderful.

RyanfaeScotland - I give up. What's the punchline?

-- TTK
ttk

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Re: 1047: "Approximations"

Klear wrote:
Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.

How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.

What do you get if you multiply six by nine?

San Fran Sam

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Re: 1047: "Approximations"

deoxys9 wrote:This would make an excellent poster. I'd buy it in a heartbeat. They're just so elegant and cool!

I would as well - I'd hang it in my classroom, and try to find some fun way to incorporate it into my lessons. I'm sure the kids would get a kick out of it.
Astari

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Re: 1047: "Approximations"

somebody_else wrote:The error in the first Protip is pretty big though. If only the fractions were added instead of subtracted. I am going to use the radius of the earth one from now on - just to confuse anyone reading my work.

It's a simple error. It should be plus, not minus. 3/5 + pi/(7-pi)

/a picogalyear is about 2 hours (galactic year/10**12)
Dr. Tom

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Re: 1047: "Approximations"

San Fran Sam wrote:quote]

What do you get if you multiply six by nine?

42. I love base 13 jokes.
Elirra

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Re: 1047: "Approximations"

I take exception with the joke about 1/140... 1/137 is a perfectly fine constant approximation.

Trickster

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Re: 1047: "Approximations"

San Fran Sam wrote:
Klear wrote:
Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.

How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.

What do you get if you multiply six by nine?

fourty-two.

only with stone scrabble tiles though.
www.crashie8.com
popman

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Re: 1047: "Approximations"

My physics teachers are going to get a kick out of this one.

I also warned them in case a wiseass decided to try and use that on a test or homework.

therenaissanceman

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Re: 1047: "Approximations"

The age of the universe approximation is more like 1/160 accurate for the current WMAP 7yr value (Komatsu et al. 2011,
ApJS 192, 18).

The problem is that that measurement is a very model dependent value -- the current age estimate (13.76 +- 0.11 Gyr) makes
a bunch of assumptions (dark energy is a cosmological constant, a non running initial spectral index, purely Gaussian initial
conditions, number of relativistic neutrino species, no sterile neutrinos, etc.). There's a good chance at least one of those
will turn out to be wrong, although we don't know which one(s). None of those are likely to change the age that much
(so it won't suddenly become 11 Gyr or something), but you shouldn't believe that the age is currently measured to the
1 part in 70 that Randall claims.
aconley

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Re: 1047: "Approximations"

Aw. My favorite isn't there:

φ ≈ -2sin(666°)

The golden ratio is the doubly negative sine of the beast.

Don't know exactly how accurate it is (or even if it's exact); a cursory calculation or two and comparison shows it's at least 8 digits accurate.
praetor_alpha

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Re: 1047: "Approximations"

He left off that the speed of light is (3+ln(20))/2 * 10^8 meters/second, correct to 1 part in 50000.
Last edited by Wnderer on Wed Apr 25, 2012 8:53 pm UTC, edited 1 time in total.

Wnderer

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Re: 1047: "Approximations"

I have a 'proof' published about 60 years ago of why the proton/electron rest mass is 6{{\pi }^{5}},

It was publised in "Imperfect picture: An appreciation of the scientific and philosophic thought of Alfred Claude Jessup". I posted it at:

http://nigel.thedyers.org.uk/Jessup/Imperfectpicture.pdf
AnotherAngle

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Re: 1047: "Approximations"

The value of second per/year approximation in the header of the page (just below the xkcd logo) is shown as pi * 10^6. The value of pi * 10^7 is 31,415,926. It's an off-by-one error, we all get 'em.
tangozulu

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Re: 1047: "Approximations"

Hmm, I like e^π - π = 20. I already made people think their calculators have floating point errors like Intel CPUs...
MichiK

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Re: 1047: "Approximations"

This reminds me of my applied physics class and error analysis. We would go through and work out the percentage errors assuming certain errors in our measurements. Of course we assumed the constants had no errors, and in fact the precision of the constants were much higher than the precision of the measurements, so error attributed to constants were negligible. It would be interesting to do such an analysis to see if any of these approximations would lead to significant increases in the error of the experiments.

Which of course is the real metric of an approximation. Constants do not exist by themselves. They are used to infer additional results. For instance, the gas constant allows us to convert the energy represented by temperature in an amount of ideal gas to the actual energy. The number itself is an experimental contrivance determined by a fit.

I guess it annoys me a little then to focus on these numbers themselves, since the numbers are not nearly as interesting as the process used to generate the numbers. I guess that is the experimental part of me rebelling against the ivory tower mathematicians, some who seem to be looking for cosmological significance in the fact everything can be approximated with pi or e or whatever is the constant of the day. Of course it is all in fun, and it is certainly enlightening to seeing the devine in e^(i*pi), but at the end of the day I would rather be looking for such things in a laser beam bouncing around the room, or an electron circulating a magnetic field, than in a bunch of numbers.
rcox1

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Re: 1047: "Approximations"

I this is the first time in have absolutely no idea what this comic means, and that the comments here don't help in any way, shape or form.
I mean, utterly clueless. (I get Jenny's number, but none of this math/science is remotely ineligible. Oh well. First for everything.
Leshy

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