- #1

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Pi day is tomorrow! 3.14!

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

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

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- Thread starter Greg Bernhardt
- Start date

- #1

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Pi day is tomorrow! 3.14!

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

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

- #2

DrClaude

Mentor

- 8,022

- 4,750

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

- #3

- 17,645

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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.Pi day is tomorrow! 3.14!

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

- #4

Borek

Mentor

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(where P are primes and N are natural numbers)

- #5

A pie pi wide is pi square round.

- #6

OCR

- 953

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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... .

.

(BTW, Greg... thanks for the reminder)

Still married to the same one,

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

.

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- #7

AlexCaledin

- 361

- 578

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- #8

jobyts

- 218

- 58

Q. What is the volume of a pizza with radius z and thickness a?

A. pizza

A. pizza

- #9

- #10

epenguin

Homework Helper

Gold Member

- 3,959

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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

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.

(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

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- #11

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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.At what level would one have to be for it to be 'not that complicated'?

- #12

Fig Neutron

- 61

- 95

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 ).

- #13

AlexCaledin

- 361

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"May I have a large container of coffee"

- this is stronger than coffee :

- #14

david2

- 29

- 84

Current world record:70030(!) digits.

http://pi-world-ranking-list.com/index.php?page=lists&category=pi

- #15

- 23,780

- 15,390

Current world record:70030(!) digits.

http://pi-world-ranking-list.com/index.php?page=lists&category=pi

Changing to ##\tau = 2\pi## would be worthwhile just to highlight the pointlessness of that if nothing else.

- #16

david2

- 29

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You are right.It is pointless.But still quite impressive what the human mind can do.

- #17

- 10,101

- 10,677

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

- #18

Borek

Mentor

- 29,168

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

Aliens!

- #19

- 10,101

- 10,677

Even worse - numerologist aliens.Aliens!

- #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

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- #22

Gigel

- 27

- 6

On the other hand, two pies are better than one.Changing to ##\tau = 2\pi## would be worthwhile just to highlight the pointlessness of that if nothing else.

Is there a constant called cookie?

- #23

- 17,645

- 18,325

Just found

(where P are primes and N are natural numbers)

$$\int_0^1 \frac{\log x}{x-1} \,dx = \frac{\pi^2}{6}$$

I don't like this Pythagorean numerology in me, but I can't escape its fascination. What is it with this ##\pi^2/6\,##?

- #24

Asymptotic

- 782

- 528

Current world record:70030(!) digits.

http://pi-world-ranking-list.com/index.php?page=lists&category=pi

Not to so many digits, but pi, when sung, can captivate the ear.

- #25

TeethWhitener

Science Advisor

Gold Member

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Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##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\,##?

- #26

- 17,645

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Sure. I just wanted to emphasize the visual beauty of the three different expressions by ##\sum\; , \; \prod\; , \;\int##Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##

- #27

- 17,645

- 18,325

The following sentence about ##\pi## has been stable under Google-Translate transformations:

"Pi is not included in any Galois extension of rational numbers."

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