I find Pi very interesting and mysterious.
It goes like 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...................................................................... to infinity.

Pi is an irrational number, meaning it has an infinite, non-repeating decimal expansion.
Fun fact is that it contains our Contact number,Passwords,Date Of Birth etc somewhere in those numbers.

It also comes in many equations of physics.
Everything is mostly spherical in our universe due to gravity.
So pi is everywhere as pi is used in calculations involving spheres.
I also saw a theory in speculations which is now locked,it was built around pi.

I was thinking that maybe Pi can be used for more things in our universe.Maybe its key to something bigger.

What do you think?

Just now, Dhillon1724X said:

What do you think?

I think you need to know a little bit more about numbers before you can appreciate the answers

Some nmembers, including myself, tried to steer you towards this in earlier threads.

Firstly Pi is indeed an irrational number, but that does not mean what you claim at all.

1/3 is an irrational number that repeats forever in the decimal expansion.

Pi is more than that it is trancendental, which means it does not repeat.

That is in simple terms the difference between irrational numbers and trancendental numbers like Pi.

But there is more to it than that.

I assume you know what integer numbers are and what their properties are.

But what do you know about the rational numbers and their properties ?

How much do you know about irrational number is and how they differs from integers and rational numbers ?

9 minutes ago, Dhillon1724X said:

I find Pi very interesting and mysterious.
It goes like 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...................................................................... to infinity.

Pi is an irrational number, meaning it has an infinite, non-repeating decimal expansion.
Fun fact is that it contains our Contact number,Passwords,Date Of Birth etc somewhere in those numbers.

It also comes in many equations of physics.
Everything is mostly spherical in our universe due to gravity.
So pi is everywhere as pi is used in calculations involving spheres.
I also saw a theory in speculations which is now locked,it was built around pi.

I was thinking that maybe Pi can be used for more things in our universe.Maybe its key to something bigger.

What do you think?

It is not only irrational but a transcendental number, like e. And there is a famous and mysterious connection between the two of them known as Euler's identity:

This is connected with the polar form of complex numbers, i.e. r(Cos𝜽 +iSin𝜽).

Edited July 29Jul 29 by exchemist

9 minutes ago, studiot said:

but that does not mean what you claim at all.

I am not claiming anything.Its a discussion thread.
Here i can learn.

13 minutes ago, studiot said:

But what do you know about the rational numbers and their properties ?

How much do you know about irrational number is and how they differs from integers and rational numbers ?

A rational number is any number that can be expressed as the ratio of two integers
Their properties-
Decimal expansions either terminate or repeat
Closed under addition, subtraction, multiplication, and division (except division by zero)

Irrational numbers cant be expressed as ratios
their properties-
Decimal expansions: non-terminating, non-repeating

Transcendental Numbers is a subset of irrational numbers

2 hours ago, studiot said:

1/3 is an irrational number [...]

No. The definition of an irrational number implies that:

"That is, irrational numbers cannot be expressed as the ratio of two integers."

https://en.wikipedia.org/wiki/Irrational_number

1/3 can be expressed as the ratio of two integers..

https://en.wikipedia.org/wiki/Rational_number

"a rational number is a number that can be expressed as the quotient or fraction ⁠ p / q ⁠ of two integers, a numerator p and a non-zero denominator q.[1] For example, ⁠ 3 / 7 ⁠ is a rational number, as is every integer"

Edited July 29Jul 29 by Sensei

Just now, Sensei said:

No. The definition of an irrational number implies that:

"That is, irrational numbers cannot be expressed as the ratio of two integers."

https://en.wikipedia.org/wiki/Irrational_number

1/3 can be expressed as the ratio of two integers..

https://en.wikipedia.org/wiki/Rational_number

"a rational number is a number that can be expressed as the quotient or fraction ⁠ p / q ⁠ of two integers, a numerator p and a non-zero denominator q.[1] For example, ⁠ 3 / 7 ⁠ is a rational number, as is every integer"

Gosh that was a silly mistake, a very silly mistake.

It's obviously the season for it.

Thank you for putting it right. +1

And \( \pi^{\pi} \) is likely irrational, but we don't know...

It's fun seeing all the places Pi shows up (or at least seems to).

https://www.youtube.com/watch?v=d0vY0CKYhPY

https://www.youtube.com/watch?v=6dTyOl1fmDo

Edited July 30Jul 30 by pzkpfw

16 hours ago, joigus said:

And [math]π^π[/math] is likely irrational, but we don't know...

[math]2^{\sqrt{2}}[/math] is known to be transcendental.

[math]i[/math] is not rational, but is algebraic.

[math]i^{\>\!i}[/math] is known to be transcendental.

[math]e^\pi[/math] is known to be transcendental.

It is not known whether or not [math]\pi^e[/math] is transcendental.

Edited July 30Jul 30 by KJW

3 hours ago, KJW said:

22√ is known to be transcendental.

i is not rational, but is algebraic.

ii is known to be transcendental.

eπ is known to be transcendental.

It is not known whether or not πe is transcendental.

Elementary operations between transcendental numbers will likely produce at least an irrational. But it's a case study.

On 7/31/2025 at 1:39 AM, joigus said:

On 7/30/2025 at 8:38 PM, KJW said:

[math]2^{\sqrt{2}}[/math] is known to be transcendental.

[math]i[/math] is not rational, but it is algebraic.

[math]i^{\>\!i}[/math] is known to be transcendental.

[math]e^\pi[/math] is known to be transcendental.

It is not known whether or not [math]\pi^e[/math] is transcendental.

Elementary operations between transcendental numbers will likely produce at least an irrational. But it's a case study.

The transcendental numbers [math]2^{\sqrt{2}}[/math], [math]i^{\>\!i}[/math], and [math]e^\pi[/math] I mentioned are known to be transcendental by the Gelfond-Schneider theorem, which states:

If [math]a[/math] and [math]b[/math] are algebraic numbers with [math]a \notin \left\{0, 1\right\}[/math] and [math]b[/math] not rational, then any value of [math]a^b[/math] is a transcendental number.

And in the case of [math]i^{\>\!i}[/math] and [math]e^\pi[/math], there is also the identity:

[math]e^{i\pi} = -1[/math]

However, there is no known corresponding identity for [math]\pi^e[/math], and thus it is not known whether or not this number is transcendental. But Schanuel's conjecture, if proved, would establish many nontrivial combinations of [math]e[/math], [math]\pi[/math], algebraic numbers and elementary functions to be transcendental, including [math]\pi^e[/math] and [math]\pi^\pi[/math].

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Edited August 2Aug 2 by KJW

On 8/2/2025 at 3:05 AM, KJW said:

The transcendental numbers 22√, ii, and eπ I mentioned are known to be transcendental by the Gelfond-Schneider theorem, which states:

If a and b are algebraic numbers with a∉{0,1} and b not rational, then any value of ab is a transcendental number.

And in the case of ii and eπ, there is also the identity:

eiπ=−1

However, there is no known corresponding identity for πe, and thus it is not known whether or not this number is transcendental. But Schanuel's conjecture, if proved, would establish many nontrivial combinations of e, π, algebraic numbers and elementary functions to be transcendental, including πe and ππ.

[If the above LaTex doesn't render, please refresh the browser.]

Thank you for the pointers.

Things like \( i^{i} \), \( e^{i\pi} \) or \( \left( -1 \right)^{\pi} \) I tend to see as kind of trivial (perhaps wrongly). But I didn't know about the other ones.

Pi is an interesting number, but it's not as mystical as you think.

On 7/29/2025 at 8:51 AM, Dhillon1724X said:

Pi is an irrational number, meaning it has an infinite, non-repeating decimal expansion.
Fun fact is that it contains our Contact number,Passwords,Date Of Birth etc somewhere in those numbers.

It probably does, but this has not been proven. There are lots of irrational (and indeed transcendental) numbers that do not contain every finite digit string. The simplest provable example is Liouville's constant 0.110001000000000000000001000... which has a 1 in the 1st, 2nd, 6th = 3!, 24th = 4!, etc. place and a zero elsewhere. This number is clearly irrational and can also be proven to be transcendental, but it clearly does not contain all our information in its decimal expansion.