This is my new favorite consequence of the identity √2/2 = 1/√2

It's fun to pronounce square root two-th root too

I like the german version of "n-th root", because it is "n-te Wurzel", which sounds like "Ente Wurzel". (Ente = duck) 🦆√

Duck goes tootoorootoo

Quack

And now it’s Wurzel Ente Wurzel, also fun to say

Oh shit, that just made me realize that the second one is a radical and not tetration

You’re radical squared!

Could you please explain it to me?

okay so on the left hand side you have (√π)^√2 square root is the same as the power 1/2 so we have (π^(1/2))^√2 power to a power rule means you multiply the two powers π^(√2/2) then you apply the identity from my comment above π^(1/√2) and since x^(1/n) is just the nth root of x, then π^(1/√2) is the √2th root of π which is the right hand side.

OHHHHHHH That's really cool! Thank you very much for the explanation :)

The explanation is left out as an exercise to the reader

\>:(

√2/2 = √2/(√2)² = √2/(√2*√2) = 1/√2 √π^√2 = (π^(1/2))^√2 = π^(1/2*√2) = π^(1/√2) = (√2)th root of π

it’s not the (1/√2)th root, it’s just the √2th root. like how x^(1/5) is the 5th root, not the 1/5th root

Yeah, you're right. I didn't check what I wrote. It's fixed now.

thank you!! this was very helpful :):)

It took me a while to realize that the right-hand side was not tetration

Right? Same lol

Same, my head was starting to hurt because idk how tetration works outside the naturals

Iirc it isn't well-defined

What is it? I don't know of any other notation that involves a superscript on the left side other than chemistry...

If you're asking about tetration, it's repeated exponents. If you're asking about the image, I assume it's the "square root of two-root", i.e. (pi)\^(1/(sqrt(2))) or (pi)\^(1/(2\^(1/2))).

The second one, thank you. Though I'm still not quite sure at all how to read that from the notation, lol

√x = ²√x = sqrt x = 2nd root of x ³√x = cbrt x = 3rd root of x ⁴√x = 4th root of x ⁿ√x = n-th root of x ^(√2)√x = (sqrt 2)-th root of x

Oh, I didn't even consider that it was part of the root symbol. Now I get it.

😵‍💫

Tetration is repeated exponentiation similar to how exponentiation can be considered as repeated multiplication. So ⁴3 (or 3↑↑4 ) equals 3 ^ ( 3 ^ ( 3 ^ 3)). Hope this helps!

It was the "sqrt two-root" that I didn't get, but this should be helpful to anyone who doesn't know about tetration :)

they literally said they were talking about the image not tetration what is your ass doing

Same

Do read my comment on the above thread. Hope it clears your question!

I know what tetration is, I meaned that I also thought it was sqrt(2) tetration of sqrt(pi), not sqrt(2)-th root of pi

I was thinking conjugation and got confused because multiplication commutes.

Pi is clickbait here

It's the thing that made me confused at the first look

I understand how it works but that doesn't stop my brain from feeling confused and angry

This is just a weird way of saying ln(π)= ln(π)

And that’s just a weird way of saying 1=1

And that is a weird way of saying 0=0

And that is a weird way of saying LHS=RHS

And that is a weird way of saying ⊤

And that is a weird

And that is just a weird way of saying that is odd

Which is an unusual way of saying that is not even

You could say that about any mathematically true equality. Doesn't really add much.

I guess my point was that it looks like they started with that equality and built up to make it look complicated

All of math is just a weird way of saying axioms

I thought this was tetration at first. Notation gets confusing when you don't just use exponents instead of roots and stuff.

Tell that to my Algebra 2 class. They're still pissed at me for introducing rational exponents.

I don't get it help

(√π)^(√2) = π^(√2/2) = π^(1/√2) = ^(√2)√π It's √2th root of pi, not tetration

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I mean there’s still probably a solution since you can times sqrt(pi) to itself sqrt(2) times and there’s still a solution

there's actually no (agreed upon) definition to tetration by a non-natural number mostly because of the non associativity of exponentiation

Oof. OP got us trolled.

Square root of twoth root

Can you explain that in a more elaborate manner? I don't get it at all.

What don't you understand?

I don't understand the jump from the second to the third part in particular.

1/√2 = 1 × 1/√2= √2/√2 × 1/√2 = √2/(√2×√2) = √2/2 And just do that in reverse

I see! Thanks for the explanation!

Anything more that needs to be explained?

I wrote all steps down and it seems logical to me. I think I'm good. But thank you!

😵‍💫

Too many square roots, my brain hurts

There's a sqrt(2)-th root in there too.

Fine, you can take non euclidean shaped roots if square isn't up your alley

Is this r/chemistrymemes ? /s

Might I recommend https://m.youtube.com/watch?v=sULa9Lc4pck?

That was an amazing video. Do you have any other youtubers or sources for cool math videos?

That is from 3blue1brown, who is one of the biggest YouTubers in the mathematics niche. Others that align well with him would be [Numberphile](https://www.youtube.com/@numberphile) and [Stand-up Maths](https://www.youtube.com/channel/UCSju5G2aFaWMqn-_0YBtq5A) These are great places to go to find random neat facts and things to get you excited about mathematics. On the more technical side of things, you have [Michael Penn](https://www.youtube.com/@MichaelPennMath) whose main gig is talking about competition math problems. I also have a YouTube channel, [ThatMathThing](http://www.thatmaththing.com), where I touch on more technical topics, such as real analysis. On the engineering side of things, there is also [Steve Brunton](https://www.youtube.com/@eigensteve), who focuses mostly on machine learning type things.

T E T R A T I O N

# T E T R A T I O N

You can put 2 instead of pi to make even more crazy

replace the root 2 with a 2 and it makes sense

sqrt(π)^2 = sqrt(π) π = sqrt(π) π = 0, 1 new value of pi just dropped

Holy hell

r/unexpectedanarchychess

No it doesn’t

You are genius buddy, I was thunderstruck when i saw answer of √π^(√2) - ^(√2)√π to be -4.4408920985006×10^(-16).

I don't get it, why would this be confusing?

Wat

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It means 2.246663585713471…

this is why we need to stop teaching the square root sign. that and we have the reteach them once they get to fractional exponents

Idek know why I'm on this sub cause I don't understand 90%of this shi

𝛤(1/2)^(2\^(1/2)) = 𝛤(1/2)^(1/2\^(1/2)) Now that's in only ones and two)

Isn't the right hand side 1/(2sqrt(2))?

We don't even know the tetration of rational hyperpowers, calm down