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Science Memes @mander.xyz

fossilesque @lemmy.dbzer0.com

3d ago

omg

36 comments

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

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 = x1/2 * x1/2
  x/ x1/2 = x1/2

The other way around you get √

(I can't even draw simple stuff...)
- You like installing arch don't you, you're an arch installer aren't you
  
  Also, i use fedora
- Hard to draw when you're so busy kissing boys

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.
- NOW I get it. Thanks.

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.

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

Wtf is this

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

c/mathmemes

How am I s’posed to root two this?
(Aw, gimme somethin’ I can root two!)

i too remember when i was on 8th grade

36 comments