Your most interesting fact about Pi

  • #1
18,931
9,206
Pi day is tomorrow! 3.14!

What is your most interesting fact or insight about the number Pi?
 

Answers and Replies

  • #2
DrClaude
Mentor
8,022
4,750
That ##\tau (= 2\pi)## would have been a better choice :-p
 
  • Like
Likes dRic2, ohwilleke, DennisN and 1 other person
  • #3
fresh_42
Mentor
Insights Author
2022 Award
17,645
18,325
Pi day is tomorrow! 3.14!

What is your most interesting fact or insight about the number Pi?
Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.
 
  • #4
Borek
Mentor
29,168
3,844
[tex]\frac {\pi^2} 6= \sum_N \frac 1 {n^2} = \prod_P(1-\frac 1 {p^2})^{-1}[/tex]

(where P are primes and N are natural numbers)
 
  • Like
Likes cnh1995, dRic2, ohwilleke and 2 others
  • #5
A pie pi wide is pi square round.
 
  • Like
Likes Jehannum, cnh1995, Ibix and 3 others
  • #6
OCR
953
876
I got married on Pi Day 3.141987... . :smile:
(BTW, Greg... thanks for the reminder)

Still married to the same one, two too... . :biggrin:



Pi Day 3.142018 is also the day the great physicist Stephen Hawking died, at age 76... . :frown:

.
 
Last edited:
  • #7
AlexCaledin
361
578
61iR8qY7AML._SL500_.jpg


Be Rational, Get Real - NEW Funny Humor Joke POSTER
 

Attachments

  • 61iR8qY7AML._SL500_.jpg
    61iR8qY7AML._SL500_.jpg
    16.3 KB · Views: 511
Last edited:
  • Like
Likes PeroK, BillTre, ohwilleke and 3 others
  • #8
jobyts
218
58
Q. What is the volume of a pizza with radius z and thickness a?

A. pizza
 
  • Like
Likes nuuskur, cnh1995, PeroK and 6 others
  • #9
Fig Neutron
61
95
39f4bf13efa51c1eee9f5c145ba6035f.jpg
 

Attachments

  • 39f4bf13efa51c1eee9f5c145ba6035f.jpg
    39f4bf13efa51c1eee9f5c145ba6035f.jpg
    13.8 KB · Views: 453
  • Like
Likes cnh1995, PeroK, Filip Larsen and 3 others
  • #10
epenguin
Homework Helper
Gold Member
3,959
996
Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.

At what level would one have to be for it to be 'not that complicated'? I first read about it quite young, still at school, in Eric Temple Bell's book on the great mathematicians, in the chapter on Hermite by which time, well into the 19th-century It was all getting rather intimidating and oppressive, everything above one's head. But Temple Bell (funny name) had a knack of phrases which somehow stuck in the mind. Even when they were, as in this case, not his.

Charles Hermite was first to prove the transcendence (? transcendentiality?) of a 'naturally occurring' number, i.e. one not invented for the purpose of proving transcendence, i.e. .I suppose for proving existence of such numbers. The number was ##e##. The memorable phrase I still remember without having the book by me was when he said, someone should be able to prove the trancendence of π "but believe me, dear friend, it will not fail to cost them some efforts.'

Having written that, I was curious to trace the original quotation, which today the miracle of Internet allows me to do from home, allows me to do at all.

Je ne me hasarderai point à la recherche d’une démonstration de la transcendance du nombre π. Que d’autres tentent l’entreprise. Nul ne serait plus heureux que moi de leur succès. Mais, croyez m’en, mon cher ami, il ne laissera pas que de leur en coûter quelques efforts.

(Some phrasing there sounds slightly antique to me, can someone confirm?) But if one of the most famous mathematicians of all time said that of one of most famous problems (impossibility of squaring the circle in Euclidean geometry depends on it), it's not sounding "wasn't that complicated". But maybe somebody has discovered a simpler way? Accessible to ordinary mortals? Is there a standard way of doing it?
 
Last edited:
  • #11
fresh_42
Mentor
Insights Author
2022 Award
17,645
18,325
At what level would one have to be for it to be 'not that complicated'?
It had been at the end of a lecture script of Linear Algebra. I just don't remember whether it was at the end of the first semester or at the end of the first year.
 
  • #12
Fig Neutron
61
95
You can remember the first 8 digits of pi by counting the letters of each word in the sentence "May I have a large container of coffee".

Albert Einstein was born on March 14 (Pi Day).

The first 6 digits of pi appear in order 6 times (I think it's 6) in the first ten million digits of pi.

I know the thread title said "your most interesting fact", but can you tell I like pi? I have memorized all of the digits of pi (right now I'm just working on getting them in order :smile: :wink:).
 
  • Like
Likes nuuskur, DrClaude, AlexCaledin and 1 other person
  • #13
AlexCaledin
361
578
"May I have a large container of coffee"

- this is stronger than coffee :
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics :skullXbones:
 
  • Like
Likes DrClaude and Fig Neutron
  • #16
david2
29
84
You are right.It is pointless.But still quite impressive what the human mind can do.
 
  • Like
Likes Asymptotic and fresh_42
  • #17
Ibix
Science Advisor
Insights Author
2022 Award
10,101
10,677
To better than 0.5%, a year is ##\pi\times 10^7## seconds.
 
  • #18
Borek
Mentor
29,168
3,844
To better than 0.5%, a year is ##\pi\times 10^7## seconds.

Aliens!
 
  • Like
Likes Ibix and DennisN
  • #20
Gigel
27
6
Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.


##\pi = - i \ \ln(-1)## or ##\pi = - 2 \ i \ \ln(i)##

There you have it. :)
 
  • #21
DennisN
Gold Member
1,934
6,142
37702f50-cb9e-0133-971f-0ec2e53676a1.jpg
 

Attachments

  • 37702f50-cb9e-0133-971f-0ec2e53676a1.jpg
    37702f50-cb9e-0133-971f-0ec2e53676a1.jpg
    24.8 KB · Views: 386
  • Like
Likes nuuskur and Ibix
  • #22
Gigel
27
6
Changing to ##\tau = 2\pi## would be worthwhile just to highlight the pointlessness of that if nothing else.
On the other hand, two pies are better than one.

Is there a constant called cookie?
 
  • #23
fresh_42
Mentor
Insights Author
2022 Award
17,645
18,325
[tex]\frac {\pi^2} 6= \sum_N \frac 1 {n^2} = \prod_P(1-\frac 1 {p^2})^{-1}[/tex]

(where P are primes and N are natural numbers)
Just found
$$\int_0^1 \frac{\log x}{x-1} \,dx = \frac{\pi^2}{6}$$
I don't like this Pythagorean numerology in me, but I can't escape its fascination. What is it with this ##\pi^2/6\,##?
 
  • #25
TeethWhitener
Science Advisor
Gold Member
2,439
1,982
Just found
$$\int_0^1 \frac{\log x}{x-1} \,dx = \frac{\pi^2}{6}$$
I don't like this Pythagorean numerology in me, but I can't escape its fascination. What is it with this ##\pi^2/6\,##?
Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##
 
  • #26
fresh_42
Mentor
Insights Author
2022 Award
17,645
18,325
Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##
Sure. I just wanted to emphasize the visual beauty of the three different expressions by ##\sum\; , \; \prod\; , \;\int##
 
  • #27
fresh_42
Mentor
Insights Author
2022 Award
17,645
18,325
How about a modern version?

The following sentence about ##\pi## has been stable under Google-Translate transformations:
"Pi is not included in any Galois extension of rational numbers."
 
  • Like
Likes nuuskur and Charles Link

Suggested for: Your most interesting fact about Pi

Replies
50
Views
1K
Replies
86
Views
2K
  • Last Post
Replies
7
Views
645
Replies
28
Views
1K
Replies
1
Views
128
Replies
20
Views
495
Replies
10
Views
506
Replies
3
Views
390
  • Last Post
2
Replies
46
Views
2K
Top