[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 17 KB, 581x538, 1539830567133.png [View same] [iqdb] [saucenao] [google]
10168319 No.10168319 [Reply] [Original]

*blocks your path*

What do you do, /sci/?

>> No.10168346

>>10168319
Just walk around, it's not very big.

>> No.10168359

>>10168319
well it can’t exist so nothing

>> No.10168398

>>10168319
[math]\sqrt{|i|^{2}+|1|^2}=\sqrt{2}\neq 0[/math]

>> No.10168484

>>10168398
Do you have to use a modulus when applying pythagoras though?

Haven't actually thought about that yet, have any proof?

>> No.10168490 [DELETED] 

>>10168484
Yes.

>> No.10168493

>>10168490
Mind sharing it anon?

>> No.10168495

>>10168484
Yes. Pythagoras says "the square of the length of C, is the sum of the squares of the LENGTHS of A and B. The square of the length of i is 1.

>> No.10168496

>>10168484
>assume you don't have to
>then there are TRIANGLES WITH SIDE FUCKING ZERO NIGGA YOU WOT

>> No.10168552

>>10168496
lol

>> No.10168573

>>10168496
Yeah but this is maths.
We can use the term >imagine

>> No.10168579

>>10168496
yeah but one of the sides is imaginary

>> No.10168585

>>10168579
The length of any complex number is real

>> No.10168607
File: 729 KB, 1084x828, out.webm [View same] [iqdb] [saucenao] [google]
10168607

im not a mathematician but idk

>> No.10168799

>>10168319
Understand you are not looking at a triangle but a matrix of defined values.

>> No.10168820

>>10168319
What if that is not a triangle, just two lines?

>> No.10169589

>>10168319
Was gonna make a snarky comment about the old definition of Minkowski metric with imaginary time, but my imaginary time had run out.

>> No.10169692

>>10168319
No.
The metric is positive definite you fucking retard.

>> No.10169694

>>10168484
You don’t need a proof. It’s part of the definition of [math]\mathbb{R}[/math] equipped with the Euclidean metric.

>> No.10169747

>>10168319
What are imaginary numbers even used for? In all my brainlet math classes (up to calc 2) they were never used in any "real world" examples/exercises. From my understanding its just like a 3rd axis on an x y graph.

>> No.10169749

>>10169747
electrical circuits with AC current

>> No.10169758

>>10169747
Calc usually doesn't cover complex numbers, but they start showing up again in diffeq's. They become a mainstay in engineering math after that.

>> No.10169760

>>10169758
>>10169749
Makes sense with their flip floppyness, thanks. I never saw them again since I am a CSlet.

>> No.10169931

>>10168607
This does not help sorry. It doesn't work like that.

>> No.10169943

>>10168495
no the square of the length is -1. the length is i. the square of i is -1. Of course, you can't assign i as a length so it's just a joke

>> No.10169966

>>10168319

shouldn't the longest side have a length of 1 ?

>> No.10169967

>>10169760
>>10169758
this isn't really an "application". It is used as a trick, i.e. representing things that way coincidentally happens to make calculations more convenient. Schrodinger equation is a better example but I am yet to find a satisfying answer as to whether it's also just a trick there

>> No.10169968

>>10169966
the op is saying Length hypotenuse is sqrt (1^2 + i^2)=sqrt(1-1)=0. but >>10169943

>> No.10170669

>>10169760
in graphics when youre using quaternions to rotate objects you get to use i.

>> No.10171840

bump

>> No.10171855 [DELETED] 

>>10168398
>>10168495
>>10169694
>>10169968

these posts are cringy bc you all are wrong and obviously aren't smarter than Einstein

>> No.10171860

>>10169967
numbers are a trick though, real or not

>> No.10171863 [DELETED] 

>>10171855
nix the 3rd post, but missing the point

>> No.10171870

dist(1+0i;0+ii)=dist(1,-1)=2

>> No.10171874

>>10168495
>>10169968

these posts are cringy bc you all are wrong and obviously aren't smarter than Einstein

>> No.10172096
File: 25 KB, 134x127, image.png [View same] [iqdb] [saucenao] [google]
10172096

1i sticks out in the third dimension, so from the 2d perspective it seems that the blue line has a length of 0

>> No.10172100

>>10168319
You're all idiot, except this guy:
>>10169589
The hypotenuse is just lightlike. The sides of length 1 and i are spacelike and timelike, though which is which depends on the metric convention.

>> No.10172103

>>10169692
The metric has indefinite signature..

>> No.10172123

>>10169747
>>10169749
>>10169758

Quantum mechanics was the first real world use of complex numbers.

Complex numbers in electrical engineering is just glorified trigonometry.

>> No.10172166

>>10172103
Not if you’re using the Pythagorean theorem you fucking brainlet

>> No.10172169

>>10172103
Also *any* full metric must preserve the triangle inequality. What OP posted is not a triangle.

>> No.10172340

>>10169747
It gives us the Fundamental Theorem of Algebra
If you're looking for "applied" like in engineering or whatever, you're a brainlet.

>> No.10173048

>>10168398
>[math]|i|^2 = 1^2[/math]
Absolute goy

By using the actual application of the operation, which is [math]|X| = \sqrt{X^2}[/math], we get [math]|i| = \sqrt{i^2} = \sqrt{-1} = i[/math]
In fact, it applies so flawlessly that even the sign of negative [math]i[/math] is successfully removed: [math]|-i| = \sqrt{(-i)^2} = \sqrt{-1} = i[/math]

But hey, let's just make the absolute value of [math]i[/math] equal to 1 because why not lmao XD

>> No.10173059

>>10173048
v = [1,1] |v| =?

>> No.10173077

>>10173059
[math]\sqrt{2}[/math]

But the length of v{i, 1} is 0

>> No.10173091

>>10173048
>what is modulus
>what is z*z

Abuse of notation. The magnitude of a complex number is the square root of itself times its complex conjugate. It's not "absolute value" anymore.

>> No.10173097

>>10173048
>>10173077
What's your iq?

>> No.10173103

>>10168607
this is the most brainlet thing I've seen all day

>> No.10173134

>>10173048
z*zconjugate = 2

>> No.10173138

>>10173091
>>10173097
>>10173134
seething

>> No.10174890

>>10168319
i=-1

>> No.10174925

>>10168319
i=-0

>> No.10174928

>>10168319
i=-)

>> No.10174948

>>10173138
>seething
Yeah, you can go back to 4chan
|z| obviously doesnt mean absolute value in this case, you supreme retard. |i| is in fact 1, and |1+i| is in fact sqrt(2). Kys.

>> No.10174956

>>10168319
i=i

>> No.10174964

>>10173077
No? Check out out length is defined

>> No.10174970 [DELETED] 

>>10168319
lol it's because i and 1 are orthogonal (one lies on the real number line, the other on the imaginary). Which means of course the hypotenuse wouldn't lie in [math]\mathbb{R}^2[\math]

>> No.10174972

>>10168319
>lol it's because i and 1 are orthogonal (one lies on the real number line, the other on the imaginary). Which means of course the hypotenuse wouldn't lie in [math]\mathbb{R}^2[/math]

>> No.10174974

>>10174948
>Yeah, you can go back to 4chan
Now I'm not a mod, but I'd ban someone for life for saying this.

>> No.10174982

>>10168319
https://math.stackexchange.com/questions/169680/pythagorean-theorem-for-imaginary-numbers

>> No.10175060

>>10173048
Because the absolute value is defined as distance from zero you fucking retard.

>> No.10175118

>>10174974
Why tho? I thought i was being clever

>> No.10175125

>>10174974
This is 4channel, you racist bigots need to go back to 4chan so heroshima can earn moeny to hire a harem

>> No.10175163

>>10175118
>4channel elitism
I smiled when i read it.

>> No.10176244

>>10168319
Remember it can't exist and keep walking

>> No.10176277

>>10168484
There are no negative distances. See the definition of any metric space.

>> No.10176283

>>10169943
the length of i is i.
Citation needed. https://www.wolframalpha.com/input/?i=%7Ci%7C

>> No.10176951

byampu~~~~~~~~~~

>> No.10177408

laugh in engineer and tell it to come back when drawn to scale

>> No.10177509

>>10168398
Math big boy here.

I'm going to give a spoiler. The definition of Pythagoras's theorem that would extend to complex lengths is:

[math]x= \sqrt{ z \overline{z}+ y \overline{y}} [/math]

I leave it to 4chan to prove why.

>> No.10177585

>>10177509
cringe

>> No.10177595

>>10177509
Or you could just use absolute values instead of flexing that you know what conjugates are (lol) retard

>> No.10177859

>>10168319
it can't exist therefore there can be no answer

>> No.10178072
File: 113 KB, 1131x622, 1534637873918.jpg [View same] [iqdb] [saucenao] [google]
10178072

>>10168319

>> No.10178310

>>10168319
Rotate the triangle so that the only side you can see is the one of length 1 and it looks like a line. Now it makes sense.

>> No.10179060

>>10168398

This.

You treat the y-axis as real numbers for the purpose of calculating the hypotenuse >>10168319 you absolute brainlet

>> No.10179068

>>10168319
sounds legit

>> No.10179457

>>10172169
We're using "metric" in two different sense here

>> No.10179471
File: 102 KB, 911x1024, 1543495842639.jpg [View same] [iqdb] [saucenao] [google]
10179471

>>10168319
So I've seen this shitpost before and seen this https://en.wikipedia.org/wiki/Minkowski_space being linked in the thread
Can someone who's not a brainlet and who can actually understand it explain it? Is it imaginary lengths being applied irl or something?

>> No.10179575

>>10179471
You're looking too deep into it. The pythagorean theorem is concerned with LENGTHS making OP's hypothenuse be √(|i|^2 + 1^2) = √(1^2 + 1^2) = √(1 + 1) = √2.
Ignore the uneducated trolls saying that |i| doesn't exist (https://www.wolframalpha.com/input/?i=%7Ci%7C).). Even if you consider the sides of the triangle as vectors, then the result is still √2 and not 0. I'm not sure why this image baits /sci/ so much.

>> No.10180237
File: 40 KB, 557x447, D9216822-7CEF-437A-9524-7EBF1532CF1D.jpg [View same] [iqdb] [saucenao] [google]
10180237

>>10177509
wtf is up with 4chan's latex?

>> No.10180726

>>10168319
[math]d(i,1)=\sqrt{\langle i-1, i-1\rangle}=\sqrt{(i-1)(-i-1)}=\sqrt{2}[/math]

>> No.10182268

bümp

>> No.10182292
File: 43 KB, 1790x512, capture.jpg [View same] [iqdb] [saucenao] [google]
10182292

>>10180237
looks fine

>> No.10182309

>>10176283
i meant that on the picture, the labelling implies that "i" is the length of that side. As I said of course it isn't. That's the meme. The length of the side is the length of the vector from 0+0i to 0+1i which is 1

>> No.10182339

>>10182309
>abloo abloo complex lengths dont exist in reality
see: https://en.wikipedia.org/wiki/Imaginary_time

>> No.10182430

>>10182339
what does that have to do with length? (btw what a cringy article, the editor all defensive/butthurt about "imaginary" meaning made up)

>> No.10182538

>>10173059
imagine providing a vector counter example to a solution entirely NOT about vectors.