1 • 1 + i • i = 1 + (-1) = 0 = 0 • 0
Pythagoras holds, provided there’s a 90° angle at A.
Fuck geometry
Submitted 5 months ago by muntedcrocodile@lemm.ee to science_memes@mander.xyz
https://lemm.ee/pictrs/image/b7195764-54c9-4be2-b457-9f38acd45ae7.jpeg
Comments
manucode@infosec.pub 5 months ago
blackberrynoseferatu@lemmy.world 5 months ago
this is why it is still a theorem
suzune@ani.social 5 months ago
I’m so angry at people who think that distances can be imaginary.
Xerodin@lemm.ee 5 months ago
When talking about AC power, some of the power consumed doesn’t actually produce real work. It gets used in the generation of magnetic fields and charges in inductors and capacitors.
The power being used in an AC system can be simplified by using a right triangle. The x axis is the real power being used by resistive parts of the circuit (in kilowatts, KW). The y axis is reactive power, that is power being used to maintain magnetic fields and charges (in kilovolt-amperes reactive, KVAR). And the hypotenuse is the total power used by the circuit, or KVA (kilovolt-amperes).
Literal side note: they’re all the same units, but the different sides of the triangle are named differently to differentiate in writing or conversation which side of the power triangle is being talked about. Also, AC generator ratings are given in KVA, so you need to know the total impedance of your loads you want to power and do a bit of trig to see if your generator can support your loads.
The reactive component of AC power is denoted by complex numbers when converting from polar coordinates to Cartesian.
Anyways, I almost deleted this because I figured your comment was a joke, but complex numbers and right triangles have real world applications. But power triangles are really just simplifications of circles. By that I mean phasors rotating in a complex plane, because AC power is a sine wave.
lugal@lemmy.dbzer0.com 5 months ago
Never been together with people and still felt alone?
Brainsploosh@lemmy.world 5 months ago
They’re about as imaginary as numbers are in general.
Complex numbers have real application in harmonics like electronics, acoustics, structural dynamics, damping, regulating systems, optronics, lasers, interferometry, etc.
In all the above it’s used to express relative phase, depending on your need for precision you can see it as a time component. And time is definitely a direction.
technocrit@lemmy.dbzer0.com 5 months ago
You’re mad at mathematicians for constructing complex valued metrics?
Foofighter@discuss.tchncs.de 5 months ago
But that’s not the definition of the absolut value, I.e. “distance” in complex numbers. That would be sqrt((1+i)(1-i)) = sqrt(2) Also the triangle inequality is also defined in complex numbers. This meme is advanced 4-4*2=0 Works only if you’re doing it wrong.
DavidGarcia@feddit.nl 5 months ago
I get it, it’s projected on a comlplex sphere. B and C are the same point
luciole@beehaw.org 5 months ago
please stop making it make sense
model_tar_gz@lemmy.world 5 months ago
You didn’t really expect an imaginary triangle to behave like a real one, did you?
EtherWhack@lemmy.world 5 months ago
A and B have a wormhole between them
xylogx@lemmy.world 5 months ago
In the complex plane each of these vectors have magnitude 1 and the distance between them is square root of two as you would expect. In the real plane the imaginary part has a magnitude of zero and this is not a triangle but a line. No laws are broken here.
propter_hog@hexbear.net 5 months ago
i = 1is the only logical choiceDragonTypeWyvern@midwest.social 5 months ago
Literally, this is one of those questions where they’re testing logic and your understanding that the figures aren’t necessarily representative of physical reality.
i_love_FFT@jlai.lu 5 months ago
I kept seeing this pop up recently, and I finally understand it: it’s an introductory problem in Lorentzian general relativity.
AB is a space-like line, while AC is a time-like line. Typically, we would write AC as having distance of 1, but with a metric such that squaring it would produce a negative result. However it’s similar to multiplying i to the value.
BC has a distance of 0, but a better way of naming this line would be that it has a null interval, meaning that light would travel following this line and experience no distance nor time going by.
I’m sure PBS Spacetime would explain all of this better than me. I just woke up and can’t bother searching for the correct words on my phone.
ShinkanTrain@lemmy.ml 5 months ago
It gets worse once you start doing trig on it
technocrit@lemmy.dbzer0.com 5 months ago
Maybe the problem is constructing a metric that makes this diagram true. Something like d(x,y) = | |x| - |y| | might work but I’m too lazy to check triangle inequality.
stevedice@sh.itjust.works 5 months ago
Triangle inequality for your metric follows directly from the triangle inequality for the Euclidean metric. However, you don’t need a metric for the Pythagorean Theorem, you need an inner product and, by definition, an inner product doesn’t allow non-real values.
deikoepfiges_dreirad@lemmy.zip 5 months ago
funny Interpretation: in the complex plane, the imaginary axis is orthogonal to the real axis. so instead of the edge marked with i, imagine an edge of length one orthogonal to that edge. It would be identical to the edge marked with one, so the distance between the ends of the edges is zero.
propter_hog@hexbear.net 5 months ago
But then CB couldn’t also be 0; wouldn’t it be
cos(1 + i)? Or something like that.deikoepfiges_dreirad@lemmy.zip 5 months ago
oh I mixed up the points, I meant to say CB is 0 in the end
Lemmygradwontallowme@hexbear.net 5 months ago
Wish me luck for I’m doing trig test with radians (2 pi rad ?)
muntedcrocodile@lemm.ee 5 months ago
Radians are the objectivly better way to do angles tho. Just remeber π=180deg and ur right. Btw here is a another brain fuck the units radians/second is just Hz
Lemmygradwontallowme@hexbear.net 5 months ago
Thank you for reminding me!
Btw, Radians/sec = Hz? What is this, physics?
Zagorath@aussie.zone 5 months ago
Radians are the objectivly better way to do angles
Yes, and tau is objectively better than pi. Just remember tau = 360°. Which is a full circle, which easier to work with than half a circle.
OrganicMustard@lemmy.world 5 months ago
You can make something like this properly by defining a different metric. For example with metric dl^2^ = dx^2^ - dy^2^ the vector (1, 1) has length 0, so you can make a “triangle” with sides of lengths 1, -1 and 0.
kogasa@programming.dev 5 months ago
That’s not a metric. In any metric, distances are positive between distinct points and 0 between equal points
OrganicMustard@lemmy.world 5 months ago
It depends which metric definition are you using. The one I wrote is a pseudo-Riemannian metric that is not positive defined. Normally physicists use that generalized metric definition because spacetime in most cases has a metric signature of (-1, 1, 1, 1). Points with zero distance are not necessarily the same point, they just are in the same null geodesic.
technocrit@lemmy.dbzer0.com 5 months ago
This is true for real-valued metrics but not complex-valued metrics.
solomon42069@lemmy.world 5 months ago
I feel violated trying to read that in my brain.
calcopiritus@lemmy.world 5 months ago
This triangle is impossible.
If the distance between B and C is 0, B and C are the same points. If that is the case, the distances between A and B and A and C must be the same.
However, i ≠ 1.
If you want it to be real (hehe) the triangle should be like this:
Drawing that on mobile was a pain.
As the other guy said, you cannot have imaginary distances.
Also, you can only use Pythagoras with triangles that have a 90° angle. Nothing in the meme says that there’s a 90° angle. As I see it, there are only 0° and 180° angles.
Goodbye, I have to attend other memes to ruin.
thomasloven@lemmy.world 5 months ago
Context matters. In geometry i is a perfectly cromulent name for a real valued variable.
Clinicallydepressedpoochie@lemmy.world 5 months ago
Oh shit, he used the word cromulent. Every one copy off this guy.
Dayroom7485@lemmy.world 5 months ago
Mad mobile drawing!!
technocrit@lemmy.dbzer0.com 5 months ago
Incorrect. There are complex valued metric spaces.
And even if we assume real valued metrics, then i usually represents the unit vector (0,1) which has distance real 1.
stevedice@sh.itjust.works 5 months ago
That’s NOT a metric. That’s a measure. Two wholly different things.
planish@sh.itjust.works 5 months ago
This is clearly meant to be a right triangle. And the distances between the points are the same (because the squares of the coordinate differences are the same), just the directions are different.
If you move 1 unit forward, turn the correct 90 degrees, and then move i units forward, you will end up back where you started.
calcopiritus@lemmy.world 5 months ago
You can’t have a distance in a “different direction”. That’s what the |x| is for, which is the modulus. If you rotate a triangle, the length of the sides don’t change.
muntedcrocodile@lemm.ee 5 months ago
Isnt it fine to assume a 90° angle its just that when u square side AC ur multiplying by i which also represents a rotation by 90° so u now nolonger have a triangle?
calcopiritus@lemmy.world 5 months ago
It’s not fine to assume a 90° angle. The distance between B and C is 0. Therefore the angle formed by AB and AC is 0°.
If the angle is 90°, then BC should be sqrt(2), not 0. Since the length of both sides is 1. sqrt(|i|^2+|1|^2) = sqrt(2).