Pi day is tomorrow! 3.14!

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

BillTre

Mentor
That ##\tau (= 2\pi)## would have been a better choice

dRic2, ohwilleke, DennisN and 1 other person
Mentor
2022 Award
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.

ohwilleke
Mentor
$$\frac {\pi^2} 6= \sum_N \frac 1 {n^2} = \prod_P(1-\frac 1 {p^2})^{-1}$$

(where P are primes and N are natural numbers)

cnh1995, dRic2, ohwilleke and 2 others
A pie pi wide is pi square round.

Jehannum, cnh1995, Ibix and 3 others
OCR
I got married on Pi Day 3.141987... .
(BTW, Greg... thanks for the reminder)

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

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

.

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AlexCaledin

Be Rational, Get Real - NEW Funny Humor Joke POSTER

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PeroK, BillTre, ohwilleke and 3 others
jobyts
Q. What is the volume of a pizza with radius z and thickness a?

A. pizza

nuuskur, cnh1995, PeroK and 6 others
Fig Neutron

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cnh1995, PeroK, Filip Larsen and 3 others
Homework Helper
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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?

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Mentor
2022 Award
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.

Fig Neutron
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 ).

nuuskur, DrClaude, AlexCaledin and 1 other person
AlexCaledin
"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

DrClaude and Fig Neutron
Homework Helper
Gold Member
2022 Award
david2
You are right.It is pointless.But still quite impressive what the human mind can do.

Asymptotic and fresh_42
2022 Award
To better than 0.5%, a year is ##\pi\times 10^7## seconds.

Mentor
To better than 0.5%, a year is ##\pi\times 10^7## seconds.

Aliens!

Ibix and DennisN
2022 Award
Aliens!
Even worse - numerologist aliens.

fresh_42 and DennisN
Gigel
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. :)

Gold Member

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nuuskur and Ibix
Gigel
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?

Mentor
2022 Award
$$\frac {\pi^2} 6= \sum_N \frac 1 {n^2} = \prod_P(1-\frac 1 {p^2})^{-1}$$

(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\,##?

Gold Member
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}##

Mentor
2022 Award
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##

Mentor
2022 Award