# Easy way to remember pi

gary350
I always have a hard time remembering pi past 3.14 but this pie makes it easy because I see pictures in my brain, I can look see 3.14159 any time I want.

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mcastillo356, atyy and PeroK

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How I wish I could recollect pi easily today
3 1 4 1 5 9 2 6 5

But somehow I also remember the 3 5 9 that follow ( from my first TI-50 )

No need! Just remember the fundamental theorem of Physics,$$\pi = e = \sqrt{g}$$

DennisN, atyy, member 587159 and 2 others
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Fixed that for you:
No need! Just remember the fundamental theorem of Physics,$$\pi \approx e \approx \sqrt{g}$$
"Close enough for government work..."

DennisN, Astronuc, Wrichik Basu and 1 other person
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2022 Award
mmmmmmmm.....pie.

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$$\sqrt{g}$$
The units on this one bother me... And no, before you ask, I never got used to Gaussian units either!

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atyy, DaveE, BvU and 1 other person
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Perhaps https://en.wikipedia.org/wiki/Piphilology has a useful sequence?.

As a young mind I was able to do around 50 decimals if I trained often enough (that was without any particual memo-technique). Now, all those years later, the first 18 has somehow gotten stuck in memory and since I rarely need more than that as an engineer I'm quite happy I put in the effort back then

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rarely need more than that as an engineer
Tell us about those rare occasions !

Gold Member
Tell us about those rare occasions !

They are pretty rare indeed. So rare, actually, that such occasion is still pending for me personally. But given how computer chips already are produced in nano-scale and humanity any time soon ought to start construction of some kind of Dyson sphere, that is, if we ever want to become a respectable member of the local community of astro-engineering civilizations, I guess is just a matter of time before those last few decimals becomes significant and THEN its going quite handy not having to look them up all the time.

BvU
mpresic3
This story may be mythical but here it is. Once upon a time, some modeler's thought it would be a good idea if all the physical and mathematical constants used in computer models could be read off a common data base. Shortly after implementation, it was found that the organization could not check out their results with others after the first few decimal places.
It turned the discrepancies were traced to the value of pi being read into the program. The error was traced to the coder who entered the value of pi in the database as 3.14. He was asked where he obtained the value. The coder took out his HP calculator and pressed the pi key. For us old time HP calculator operators, we remember the default display of constants was "fix-2", so that only the first two digits were displayed. Apparently, the coder thought this value was exact, or at least close enough.

BvU
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One of those occasions occurred today in this thread, namely @BvU, in post #2, I think it's 358 not 359. I.e. I can remember roughly 3.14159 26535 89793 23846, but my granddaughter knows about 3 times as many decimal places.

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I thought it was time to round off 😁

Anyway, @Filip Larsen was at 18 digits !

If I ever need 16 digits I use 2*arccos(0) but I do admit that's cheating

mathwonk
Gold Member
The fraction 22/7 is pretty good approximation for pi, but 355/113 is better - it's accurate to 6 decimals.

(An error of less than 1 millimeter error per kilometer).

And if you need accuracy to more than one part in a million - what the heck are you doing using shortcuts??

dextercioby
Gold Member
I use 2*arccos(0)
Sounds like your like me and you know the button you want is somewhere on the calculator, but you can't find it, so you just use another function. I never, ever, ask for "e", I find "e1" a much easier way to do it.

Gold Member
Perhaps https://en.wikipedia.org/wiki/Piphilology has a useful sequence?.

As a young mind I was able to do around 50 decimals if I trained often enough (that was without any particual memo-technique). Now, all those years later, the first 18 has somehow gotten stuck in memory and since I rarely need more than that as an engineer I'm quite happy I put in the effort back then
I seriously question any circumstance in engineering where you need 18 digits. How accurately do you know the yield strength of the steel your using, the value of the capacitor in your circuit, the fuel flow rate in your engine? Can you really measure your distances in meters to 1/100 the size of a proton?

I'm ok with people that want to play memory games for entertainment, but engineers need to know about significant digits, and the relative magnitude and accuracy of real world stuff. There's often nothing wrong with using 18 digits, but others might think you don't really understand "the art of approximation".

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Engineers use slide rules

vanhees71
Gold Member
Engineers use slide rules
They got Buzz and Neil to the moon and back. Lots of impressive stuff was built with 3 significant digits, back in the day. Granted not as impressive as what consumers can buy today. No LHC or LIGO in 1970.

More here: https://www.sliderulemuseum.com/

atyy
Gold Member
Uh oh. I've hijacked anther thread, haven't I? Sorry, I'll shut up now.

Mentor
Uh oh. I've hijacked anther thread, haven't I? Sorry, I'll shut up now.
Just slide on out before you break a rule...

DaveE
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when I have trouble remembering decimals of pi, I just fall back on the handy ramanujan formula:

Astronuc, Klystron, Wrichik Basu and 9 others
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I seriously question any circumstance in engineering where you need 18 digits.

As you should. Luckily I never claimed to be using 18 digits for anything in particular, engineering or otherwise, only that those are the number of digits that comes to mind without effort. And I have faith in people, including any budding engineers, who are reading this thread to not come away thinking they now need to include 18 digits in any of their engineering calculations.

However, what I did try to suggest with my with post considering the topic of the thread being how to remember decimals of pi (or any other useful constant for that matter) is that if you train to recite a useful number of them without any special memorization technique when you are young then I would think there is a good chance you can recite them fairly effortless later in life as well.

DaveE and BvU
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since I rarely need more than that
Ah ! Figure of speech, not to be taken literally 😁

DaveE and Filip Larsen
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[Slide rules] got Buzz and Neil to the moon and back. Lots of impressive stuff was built with 3 significant digits, back in the day.
No they didn't. There is a good account of the pre-flight computations as well as the real time actions and post-flight analysis at https://history.nasa.gov/afj/index.html.

The Apollo Guidance Computer had 14 hardware data bits, equivalent to 4.2 decimal digits, but I believe calculations were performed in a software VM in 24 bit (7.2 decimal digit) fixed precision.

Keith_McClary, Klystron and vanhees71
Homework Helper
My google research shows some 3 eras of hand computation of pi. First, Archimedes' method approximating area of a circle by that of a many sided polygon, eventually yielding a few dozen digits. Second, Taylor series for arctan augmented by addition formulas, yielding over 100 digits. (Euler seems to have published variants of this method but not to have actually calculated any himself. Interestingly in his book on Analysis of Infinities, he simply states the first 120 or so digits of pi, with an error (only) in about the 112th place.) Third, sophisticated formulas of Ramanujan, including the comparatively simple one above in post #21.
I just checked it for k=0, i.e. only using one term of that series, and I got 6 decimal places of accuracy, roughly 3.14159273, and two more with a second term. (Google says that I should get 8 more places of accuracy with each term, so my calculator is off somewhere.)

To top that with the elegant series pi/4 = 1 -1/3 + 1/5 -1/7 ..., seems naively to take about a million terms!

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dextercioby
gary350
No need! Just remember the fundamental theorem of Physics,$$\pi = e = \sqrt{g}$$

e = energy?

g = gravity?

$$e = \sum_{n=0}^\infty \frac{1}{n!} = \lim_{m\rightarrow \infty} \left(1+ \frac{1}{m} \right)^m \approx 2.718281828459045$$whilst ##g## is the gravitational field strength on the Earth's surface, which as pointed out by @Infrared must in this case be the dimensionless value of that quantity when expressed in the SI, to maintain dimensional homogeneity.

I might take this opportunity to mention that, in case anyone didn't notice, the fundamental theorem of Physics isn't particularly fundamental. Or a theorem, for that matter.

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member 587159
Mentor
e = energy?

g = gravity?
e is the Euler number, the base of the natural logarithm
g is the acceleration due to gravity (about ##9.81 \frac{\text m}{\text{sec}^2}## or about ##32.2 \frac{\text {ft}}{\text{sec}^2}##)

Mikestone
There's an old poem about it.

Sir, I bear a rhyme excelling
In mystic verse and magic spelling
Celestial sprites elucidate
All my own striving can't relate

Just count the letters in each word.

BvU and DaveC426913
Gold Member
I remember how to press π on my calculator. Pi is ca 3 if my memory serves me.

BillTre and Keith_McClary
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