omg

x^2
—— = x
x

Proof?

ETA: Quick verification.

x² - x² = 0 and x - x = 0, then 0 = 0 and uh... again.
- If you're saying two variables are equal, then x=x is valid. The only issue with this is it doesn't indicate the restriction at x=0. This is a "hole" in the function since anything/0 is undefined. For all other cases the equation holds true.
- x = x^1/2 * x^1/2
  
  x/ x^1/2 = x^1/2

If you crop the extra white space at the top, this meme has the √2̅:1 (or 2:√2̅) aspect ratio, which I find more pleasing than the "golden ratio", perhaps because I'm so used to A4 paper

What if I told you that it works for any number 𝑥 you replace 2 with? (Except for 0 but still working for 𝐥𝐢𝐦 𝑥→0)

... where x is positive.

Otherwise it has an imaginary component and is complex.
- Nope, it still works even then.

The other way around you get √

(I can't even draw simple stuff...)

Hard to draw when you're so busy kissing boys
You like installing arch don't you, you're an arch installer aren't you
- Also, i use fedora

Observe the identities

a / b = a × b^(-1)   (A)

sqrt(a) = a ^ (1/2)  (B)

a^b × a^c = a^(b+c)  (C)

(a^b)^c = a^(b × c)  (D)

and derive

  2 / sqrt(2)
= 2 / 2^(1/2)           (B)
= 2 × [2^(1/2)] ^ (-1)  (A)
= 2 × 2^(1/2 × (-1))    (D)
= 2 × 2^(-1/2)
= 2 ^ [1 + (-1 / 2)]    (C)
= 2 ^ (1/2)
= sqrt(2)               (B)

Neat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2) shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol
- No, that’s a mistake. Incredible how many mistakes one can make in a simple derivation.
  
  Thanks for pointing it out.

Wtf is this

It's Really simple once you get it, but it allways blows my mind.

1/sqrt(2) and 0.5 * sqrt(2) both being 0.707 always blows my mind even though it's basic algebra

This isn't intuitive to people?

2/sqrt(2) = ( sqrt(2)*sqrt(2) ) / sqrt(2)

Then cancelling out one of the sqrt(2)s in the numerator with the sqrt(2) in the denominator, you're left with sqrt(2).

I do a lot of toodling around in OpenSCAD, though, and sqrt(2) tends to come up a lot because, you know, Pythagoras and right triangles and all that.

Also pops up a lot in basic electrical engineering as the conversion factor between amplitude and RMS value of sine waves

i too remember when i was on 8th grade

c/mathmemes

How am I s’posed to root two this?

(Aw, gimme somethin’ I can root two!)