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11046749 No.11046749 [Reply] [Original] [archived.moe]

Pythagoras theorem

>> No.11046763
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>> No.11046958
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>> No.11047019

Holy shit. I just had a test and I needed to use the fact that [math] \sqrt{ a^2 + b^2 } \leq |x|+|y| [/math] but I wasn't 100% sure that it was true so I analytically proved it and it wasn't that hard but holy crap, all I needed to do was look at a goddamn triangle. Never forget your geometric intuition, children.

>> No.11047077
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11047077

>>11046749

>> No.11047084

>>11046749
Pythagoras theorem... Home...

>> No.11047088

>>11047019
But that isn't true.

>> No.11047092

>>11047088
i dont believe you

>> No.11047096

>>11047092
a=1, b=2, x=3, y=4.

>> No.11047098

>>11047088
I now see that I replaced a and b with x and y for no reason, but you get what I'm saying. If you mean that [math] \sqrt{ a^2 + b^2 } \leq |a|+|b| [/math] is not true, then I don't know what to tell you, man. You're literally looking at it.

>> No.11047099

>>11047096
Sorry, other way around.
x=1, y=2, a=3, b=4

>> No.11047110

>>11047099
>>11047096
Holy fuck you are stupid

>> No.11047114

>>11047077
|1+i|=sqrt2

>> No.11047129
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11047129

>>11047077
Well you can by definition not have complex length since [eqn]i \notin \mathbb{R}[/eqn]
and the reals is the set of all lengths in euclidean space

>> No.11047133

>>11047110
>>11047099
The mistake was mine for fucking up the notation in the first place. There's no need to be an asshole, anon. On the other side, there's also no need to be a smart-ass either, other anon.

>> No.11047149

>>11047129
What if you extend the complex numbers by adding a "hallucinatory number" h, where h is the solution to [math]|h|=-1[/math]?

>> No.11047265

>>11047149
>What if you extend the complex numbers by adding a "hallucinatory number" h, where h is the solution to [math]|h|=-1[/math]?
You could but you'd have to redefine norm in a way that allows for it to be negative but it's more useful and coincides with its current definition. And it would still make no sense talking about imaginary lengths, because lengths are real numbers greater than or equal to zero and imaginary numbers are none of those.

>> No.11047588

>>11047149
How would it work for |x+hy|, x and y real numbers?

>> No.11047597 [DELETED] 
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>>11047149
https://en.wikipedia.org/wiki/Minkowski_space

>> No.11047606

>>11047077
The illustration in this is a bit disengenuous. Since the imaginary numbers are orthogonal to the reals, the side with length i would now point back along the side with length 1 (in order to keep the 90° angle) so the image would make sense.

>> No.11047660

>>11047110
They're correct w.r.t the original equation.

>> No.11047662

>>11047588
I assume |x| - h|y|

>> No.11047696

>>11046749
Its not doing anything

>> No.11047700

>>11046958
Once again, like with the circle, the infinite staircase has infinitely many deviations from the line

>> No.11048049

>>11046749
tan^-1(b/a)
sin(tan^-1(b/a))=b/c
csin(tan^-1(b/a))=b
c=b/sin(tan^-1(b/a))

>> No.11048774
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>> No.11048779

>>11046958
fractals will never cease to be a mindfuck

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