Like math functions the weird circles etc
Only gif!!!
does that one count?
>>840278
This is exactly what I'm doing at Uni atm, I just haven't been able to visualize it this well before.
>>840302
What course curriculum would this fall under? Calculus 2? 1?
I pretty much forgot what you even call these graphs of vectors at each point.
>>840306
It's actually a "physics" course which is actually about 50% math and 50% java programming.
We're using "Mathematical Methods for Physics and Engineering" (ISBN: 9780521679718) för the math part, IMO it's a pretty good book.
>>840310
I'm taking calc III too, but we haven't looked at a gradient field once yet.
I just looked and it is literally the next section in my book though. I guess that explains it.
Also just noticed it was using a function of (x,y), so that makes sense.
>>840312
Why java though? My "engineering programming" type class is in C.
That mashup does seem pretty interesting though.
>>840316
I dunno, technically it's theoretical physics, perhaps java is more common in that field.
Attractors
neat, i have some to dump
hmm, damn, rest of my gifs is mechanics and engineering, not pure math
>>841475
Go on.
>>841475
This is oddly soothing.
>>842367
I need more!
>>845433
>>840187
Colored version.
>>845694
>X-ray of VTEC engine.
>>847275
>>847392
>>847393
>>845700
that was mesmerizing.
>>841475
It hits the side before it goes into the dip. This gear probably wouldn't work in real life.
>>845691
it walks too sexy
>>842367
>life's problems.webm
>>847275
Sick burn
>>840273
Geometry? sure.
>>845690
that's the mechanic behind how film projectors work. Think about it. The barrels spin circularly, and the film jerks forward one frame at a time.
Here this one has circles
>>847567
Tell me you're joking.
>>849866
Some amazing shit here
blink rapidly for a neat effect
>>849879
>>849886
looks like a wave function, so it hopefully counts
it's one of those things you can make turn both ways if you look it it hard enough
>>842367
bunda
Budda bump
>>840275
cool
You guys might enjoy this.
>>>/f/2968223
Just scribble about at speed 100 a bit to get the point.
>>849226
Is it me or are all signals and systems professors super hardcore
>>849868
Can somebody explain me what a tesseract is exactly?
I understand how it's the visible "shadow" of a 4 dimensional cube in the 3D world, but how exactly did we come up to that specific form?
Would really appreciate if anybody could enlighten me on this matter
>>852180
http://jazzeria.deviantart.com/art/How-to-Draw-a-Tesseract-28094461
>>852180
we assume there is a geometrical pattern and try to continue it.
a 1d "cube" has 2 Points and 1 Line.
duplicate a 1d "cube" and move the second line into a second dimension (perpendicular to the first), tracing the points (so that what previously were the same point before duplication and moving are now connected with a line). we end up with a 2d "cube" with 4 Points, 4 Lines and 1 Face (aka a Square).
duplicate the 2d "cube" and move it perpendicularly into a third dimension, again leaving traces. now we have a 3d cube with 8 Points, 12 Lines, 6 Faces and 1 Volume.
now the thinking goes - what if we just repeat that pattern? we duplicated the 3d cube, move it perpendicularly into a fourth dimension and trace the path, so we end up with a 4d "cube" with 16 Points, 32 Lines, 24 Faces and 8 Volumes.
since we lack any sort of understanding what a fourth spatial dimension might look like and how to properly represent it, we just draw connections diagonally away from the previous vertices so the thing ends up looking like a small cube inside a large cube. but all squares are actually outside faces, we just can't draw it that way.
don't worry, the whole effort is stupid. it's quite natural to not follow this "logic". our brain is hardwired to deal with 3d stuff and 3d stuff only. that's why we can look at a 2d drawing of a cube and immediately make sense of it. we have absolutely no intiuitive concept and a severe lack of brainpower concerning anything 4d. and now trying to represent a 4d object in a 2d drawing (on paper or on screen) is just bound to fail. we would at least have to use 3d, the same way we can't represent a 3d cube properly in 1d.
>>849883
That's freaking fun to do!
>>852180
Okay short summary:
To go from 1D to 2D, you take a line segment (red) you add two adjacent line segments on the two points (green) and add one final segment opposite the original (blue). You fold it through the second dimension so all the remaining points touch, and you get a square.
2D to 3D is the same; square (red) four adjacent squared on each side (green), one opposite square (blue). Fold so the remaining edges touch and, boom, cube.
A hypercube(tesseract) is exactly the same thing. Take a cube (R), add six more cubes on each face (G), and an opposite cube (B). Fold it so that the faces touch and you get a hypercube. To get the 3D imitation-hypercube like in the gif you deform it in 3D instead. You will notice on the fake hypercube that there are only two cubes; the small inner one and the (inside-out) outer one. The remaining six cubes have to be mushed into truncated-pyramids to get all the faces to touch.
This process continues on indefinitely. For example you can make a pentaract by adding eight more tesseracts onto each of the cubes of a base tesseract, plus the opposite tesseract and folding so the remaining cubes touch.
As for the 3D tesseract being the "shadow" of the real 4D thing, that's wrong; its just a... "metaphor" to help you visualize the real thing. No idea what a hypercube's shadow would look like, but by "shadow" I assume you mean what it would look like to us if we saw one IRL. We'd probably see a cubic or rectangular-prism cross section of it depending on at what angle it intercepts 3D space, similar to how a cube produces a square or rectangle cross section in 2D.
>>841475
if you look away from this gif it slows down
>>856022
And here is a couple more images to help explain it and actually comply with the board rules.
>>856031
>>840275
is there a triangle one
>>840275
Totally reminds me of EKG and capnography waves
>>840275
the square one is tan(x)
This thread soothes my autism.
>>857245
except it isn't. tan(x) tends to infinity every pi, starting at pi/2 when cos(x) is 0
>>856827
http://i.kinja-img.com/gawker-media/image/upload/s--_6judNqq--/c_fit,f_auto,fl_progressive,q_80,w_636/18qe53qgf6cmrgif.gif
There you go. Would have just uploaded it, but it's apparently corrupt and neither 4chan's uploader nor GIMP recognize it as a gif.
>>857245
no it's not
>>857119
Wow, a periodic function reminds you of another periodic function.
>>849883
pls anon i'm tripping
>>857512
hmm, GIMP 2.8.10 didn't have a problem
good find
Septagon
Polar to Kartesian Coords
>>859464
It goes a bit too fast to follow so it ends up just being fancy
>>859475
That's true.
I slowed it a bit down, but it's still more of a fancy GIF rather than an educational.
>>859465
Is that first rotation really necessary?
>>840439
They aren't attractors. Points are leaving the region.
>>851519
dank
>>845693
That one actually took me a while to understand woud it work in real life and how old is the concept.
>>857645
triangles confirmed for shit
>>845693
This is so cool
>>862024
that's a three dimentional radian
>>861713
Do you not understand how gravity works? If they spawn outside the area the fall into the gravity well gives them enough speed to climb back out unless they get trapped. This is why orbits are ellipses and not spirals ending in collisions.
>>845700
that would make a really nice tattoo
>>862022
Thanks doc
>>862084
You do know that an attractor has a precise mathematical definition right? This has nothing to do with gravity.
Also no, if the particle starts at infinity the orbit would be parabolic, not closed. Look at any book on Kepler's problem first before you post your stupid shit.
>>862026
The surface is 2 dimensional you fucking idiot.
>>862125
Cool. So the device is a perpetual impatience machine?
>>847507
This is glorious
>>859481
especially because you don't have to construct the side twice simultaneously on both sides!
>>862026
What is non-euclidean geometry?
>>849140
Film rolls smoothly in front of a flashing light you fucking retard
>>852279
That makes sense. Thanks a lot.
HooWoo
>>861725
>how do you kill a topologist?
>hand him a mug with sprinkles on top
>>849893
Took me quite a while to realise it's rotating at all
>>851843
probably. mine's a pimp. works on brain shit
>>847567
omfg this guy
>>868210
Is this what old fags can do
>>859499
if i had to guess, it has to do with where the origin is. normally you "start" at x = 0 and let x increase when you're plotting a cartesian function, and normally you start at theta = 0 and let it increase when you're plotting a polar function.
i imagine that the first rotation has to do with the established conventions on how to translate between the two coordinate systems, and if it were not done the resulting polar graph would be shifted by half a period or something from the graph that has been established as the polar analog of that particular cartesian function.
>>859569
that being said, it's possible that with this particular function, it happens to look the same with or without the first translation and it was only included for correctness and not because it was visually necessary. that might not hold true with other functions.
>>862327
Sadly unlike you, it has depth.
>>868951
Are you fucking retarded? Are you saying the triangle has depth? Is this how much I can expect from /wsg/?
>>841464
i can't stop staring at this one
>>861717
any way you slice through this shape you always can get two circles.
>>861717
I'd like to see the plane rotate around inside the donut to see how the cross sectional shapes evolve with time.
>>868703
Pic related
>>868951
What is Elliptic geometry?
>>870021
Glad I could help.
>>870792
>>845702
oy vey
>>871127
>>841466
doesnt this suggest that pi has an end digit? I mean the circle point has to land somewhere
>>871278
No, all that suggests is that pi is a real number.
>>849871
>dat clipping tho
>>845698
I liked that and implemented it for Android.
https://github.com/pabloogc/Wub
>>871478
Nice one
>>842367
this is terrifying for some reason
>>871523
It is difficult, and sometimes impossible for humans to comprehend scale.
>>840278
>>841472
As somone with Dyscalculia I can't even begin to imagine how somone understands this stuff. I had an ex who was a maths wizz that would just say it was "easy" and shit all the time and she would never explain it. And then there is me who struggles with even the simplest sums and can't tell the time on analogue clocks.
Feels bad man
>>871523
Isn't it scarier to think the first block is infinitely small
Anyone remember that Sodaplay java thing from the 90's? Some of these remind me of that.
>>871127
This happens to me way to often when waiting at a red light
>>840273
fractals
>i'll never understand them
>>871278
someone doesn't understand the continuous number line
(dw me too)
>>852279
>we assume
Which is the point where math is lies.
>>872111
so... the whole of mathematics is lies? math is founded on axioms. hell, logic is founded on axioms, which is just a fancy word for "assumption we define as truth".
math only produces absolute truths as long as you buy into the underlying axioms. assumptions are a valid tool as long it is being made clear they're assumptions. i don't really understand your criticism of the phrase "we assume" in general.
>>841468
>o-one example is totally a proof, right guise?
>>872311
I saw a video of Neil deGrasse Tyson asking another scientist (can't think of his name) something along the lines of, "What if advanced aliens came to Earth and told us that math is the wrong way to try and make sense of the universe?"
bump
>>871753
>Dyscalculia
...that's a thing?
>>871123
just think, goyim; every vertice of a david fractal represents a dead jew at the hands of the white race!
>>847567
you cant be real..
>>857645
Vaginas
>>859569
>Just tested it with Scilab
How does that program compare to mathlab? I'm in my 3rd year of Mechanical Engineering and I've heard that next year we're going to use Scilab a lot.
>>856022
Now here is my question.
We can illustrate 3d cubes in 2d easily, you do it in your image.
Also in your image you illustrate a 4d cube in 2d.
Can we not make a 3d representation of a tesseract?
>>874446
>Also in your image you illustrate a 4d cube in 2d.
he really doesn't though. all areas defined by 4 points in a plane are squares and outside faces. all volumes defined by 8 points are non-intersecting cubes. all angles are 90°.
nothing of this is properly represented in the drawing, so it's really more of a cleaned-up artist's representation governed by how to neatly tuck everything away, rather than how it would actually look. doing a model in 3d based on that representation would just end up as a cube with the rest invisibly taking place inside. or visibly if you use translucent material.
so the trouble is twofold: 1) for an actual representation we need a fourth 90° perpendicular, but after three we've run out. 2) the 2d wireframe drawing cheats by showing us things that lie behind faces or inside volumes.
if you colour the faces of the 2d drawing, it'll look just like a cube, the same way an opaque 3d model would. which is not even a bad representation, since a 4d cube intersecting 3d space would indeed look like a 3d cube, just like a 3d cube intersecting 2d space looks like a square.
this concept is easiest shown with a sphere, so we don't have to care about orientation. if you take a 3d sphere and pass it through a 2d plane to an observer on that plane it would look like a dot growing to a circle and shrinking back to a dot. so a 4d sphere passing through our 3d space would start as a dot, expand to a sphere and shrink back do a dot before disappearing. spooky :-) i like the idea there is an infinitely larger 4d space outside of 3d space, the same way there is an infinite 3d space outside of a 2d plane and that space goes into a direction an inhabitant of the 2d plane could not hope to comprehend, because "up" or "down" is meaningless in 2d.
>>874446
You will note that to a being in 2d space the cube drawing would look like an irregular hexagon (from the outside) and the tesseract drawing an irregular octagon.
Theoretically a 4d being could make a 3d drawing that to them looked like a tesseract, but to us it would just look like some weird 3d shape.
As I stated above and >>874504 also mentioned, the best we are getting (bar some advances in cyberbrains and 4d modeling software) is 3d cross segments of higher dimensional objects
>>873715
I met the guy assistant and didn't like their thought process. They're like those things are living cause they can move on their own and said that kind of things to the public (it was at a demonstration).
I was like any living thing also needs to be able to eat to grow and to reproduce by itself but they didn't want to hear anything.
>>845700
had to watch it to the end
>>871127
What's this one?
>>849883
How can I use this to send secret messages?
>>873398
Same way that dyslexia is something too.
>>871278
The thing is that if you divide a number line into a lot of pieces you can get arbitrarily close to pi but you can never get exactly pi, you always will be off by just a little bit. Like, we define one u as 1/12th the weight of an atom of carbon, but if we try to get that with hydrogen atoms, you will find that putting 12 atoms of hydrogen together, they weigh just a little more than an atom of hydrogen.
>>872550
I don't think you know what the word "example" means. No particular numbers were used,
>>871281
Don't real numbers end?
>>849883
>all those tits
please anon, this is worksafe gif
>>875155
Not all real numbers can be represented with a finite number of decimal places, no.
>>875155
You are thinking of the rational number, which are a subset of the real numbers.
>>875233
Rationals don't end either you fagtron
1/3 = 0.333...
>>868721
kek
>>875363
Shit, you're right, my bad. I misremembered the division between rational and irrational as whether or not they terminated.
>>877947
I've seen those images in gifs before. I didn't know they were from a music video.
>>878003
The video is called The Beauty of Mathematics.It wasn't originally a music video.
>>840273
Fucking fractals. They always weird me out.
>>851447
Hehehe
>>859464
saw this on numberphile
>>862445
This.
>>862445
>smoothly
that's the illusion of motion, "you fucking retard".
jees, prove him wrong or just don't bother commenting
>>871278
The concept of infinity is a simplification of reality that is only used in math because it makes stuff easy. In reality, pi doesn't even exist because everything is quantized.
In that image, too, the dots/pixels/photons are limited.
So no, pi has no end digit, but it also doesn't really exist.
>>845691
dapper as fuck
>>880420
favourite anime
[spoiler]Triangle best girl[/spoiler]
>>873402
I don't believe that that counts as a steradian. I might be mistaken though. Last I learned, a steradian involved the 'chunk-angle' of the sphere itself, not just the surface. Anon is just posting a triangle in a way to visualize non-euclidian space. It's not supposed to take into account the curvature of the sphere/depth of the surface as if it was placed in R3.
>>849228
bump
>>880420
lol
>>862445
Dumbass,
https://en.wikipedia.org/wiki/File:Movie_projection_4_stages_en.png
>>877947
I hate to be that guy, but I think mathematics is given just a little too much credit. It's a great tool for describing just about anything, as well as making predictions. However, people so often forget that the math describes the reality. The reality has to come before the math, but people do enjoy creating reality out of math.
>>881896
Can I ask how the radius of the blue circle is formed?
Does the gradient of the point in the red line determine the curvature of it?
>>845702
what would happen if you did that with a square
>>884544
Taking a 3d sphere to 4d would be just like taking a circle to 3d. Inflate it through the 4th dimension till its spherical no mater which direction you look at it from (like how a sphere is appears circular no matter which direction you look at it from.)
For any of the platonic solids just follow the cube method: original, one on each face, opposite, fold closed. The 3d "metaphors" would (I assume) follow the 'small inner shape, truncated pyramids, large outer shape' pattern.
More complex shapes (what I assume you mean by 3d model) would follow a similar pattern (if somewhat harder to visualize).
>>845700
I love spirographs.
>>884245
the radius of curvature is the reciprocal of the curvature. The curvature is defined as the magnitude of the rate of change of the (unit) tangent vector.
>>886001
Importantly, it's the derivative with respect to the arc length parameter.
>>871278
It has to land somewhere, but 'landing' isnt a mathematical concept. Its just a way to see the definition of pi. The definition itself, calculates an irrational number.
>>883936
> I hate to be that guy
Stop being that guy.
As if there arent parts of math that lack any application.
Anyway, it was a dumb video, because Bertrand Russell meant math is beautiful on its own, and all those applications are the exact tapestries he was saying math didnt need.
>>886040
that's how these pop sci videos completely miss the point. It may be the only way to reach the masses with this stuff, but then you're giving them something diluted and perpetuating misconceptions about math and science.
>>871753
Atleast you don't have Chocula
>>847507
> camera test shot from a live action Magic Schoolbus movie
plz let me dream.
>>841475
Not used to seeing gears with such a high addendum but should work fine
>>845693
Would be easier if you showed some simulated air pressure inside
>>862508
saving this as "stepladder.gif"
>two kinds of people in the world
>>890049
saved that as "chairladder.gif"
>three or more kinds of people in the world
>>862022
It's like I'm really reading Jurassic Park
>>877947
Is there a fault at 0.35. Shouldn't the lens be other way around.
>>890472
Not only that, but the focus should be in one place only relative to the lens, not the paper.
>>845700
Pretty meh... until the end.
>>890472
No, its just the wrong lens entirely, the one in the middle has a flat side, where the one on the right has a curve on each side.
>>862327
this is why i love 4chan
>>871131
>safe_image_(1).gif
this summoned satan and made mustard gas
>>859464
it's a heptagon
>>842367
fuck off with your borg shit anon
>>842367
For some reason, the Macarena really fits well with this if you time it just right, so that AAAH-AYE hits when the finished block rolls backwards.
https://www.youtube.com/watch?v=6wINQ4ywd3U
>>840439
Quick question about attractors: Are they functions where you can find the state of a system that has gravity-like behaviour by specifying a time, rather than simulating up to that point?
>>852180
Imagine, above your head, in a completely, perfectly flat square, is a 2d realm. Everything is just flat lines.
Imagine, if you will, that you poke your finger through this realm. Because there is no depth in this realm, your finger appears as a rough circle, changing in shape as your knuckles pass through, and finally changing shape completely as your hand passes through.
Does this make sense?
Oddly enough, anime helped me here. This is a scene from the remake of Evangelion. The story requires a shit ton of explanation and it will always be 2deep4everyone, so here's the important stuff:
This thing is a 4 dimensional creature. In our world, it appears as a big blue octahedron, but you see, only a slice of it appears in our world. when it moves in the 4th dimension, it moves in seemingly impossible ways in our dimension, but that is because it is not bound by our laws. In that way, it is similar to moving your finger and arm through that 2-Dimensional realm; if any creatures were alive in that 2D realm, your arm changing 2D shape and position would seem impossible to them, but looking at it from your perspective it makes perfect sense.
Does that make sense?
>>884539
Doesn't work, that gif only works because the new shapes on the border created by the overlap are still triangles.
Or at least, it doesn't work the same way. You could makes something if you changed the method, but it wouldn't seems like a square equivalent of the pattern.
>>840278
Fuck I have my math analysis II final in two months and I can't remember any of this shit
>>875363
Rationals end, just that some of them cant be represented using the decimal system.
>>845690
https://www.youtube.com/watch?v=En__V0oEJsU
I will contribute a few
>>886091
>It may be the only way to reach the masses with this stuff
Why bother? Probably half the population does not have the requisite IQ.
>>877947
I think I got GRIDS from how fucking gay this is
>>840273
Legitimately reminds me of my first time doing acid. That shit was crazy.
>>886040
Honestly, that seems kind of dumb. Math isn't beautiful on its own, at least without reference to any real world applicability or foundation in phenomena that can be witnessed in some way. Like you can say some formula is right but if there is no way to relate that to anything can even be theoretically witnessed, then who the hell is going to think its a beautiful outside of gimmick pop-sci formulas like Tupper's self-referential formula.
>>849866
Red leader standing by
>>857645
Bottom one is false, if it were true then that's what our heartbeat would look like when it's hooked up to a machine. Clearly this isn't the case.
Myth busted.
>>871127
someone should make a webm out of this
https://www.youtube.com/watch?v=yVkdfJ9PkRQ
>>880525
But what would happen if they complete a revolution at the same speed? the smaller ones are going 2x times faster
man this thread makes me wish i stuck with maths, 15 year old me just could not be fucked
>>871753
Do you have legit dyscalculia, ore are you just intellectually lazy, liuke the rest of the normies?
>>842367
D4C!
>>900935
Here.
>>849228
i dont know why i find this so funny
>>871478
How do i use
>>902508
It's the redundancy of attaching wheels upon wheels.
>>841466
How many revolutions before π lands on another integral?
>>880523
my personal favourite is watching the gif on its own and making the leg in the middle rotate in a different direction from the rest as though it's unscrewing which is also possible
moire
>>902871
It never does that's why pi is an irrational number
>>903135
Saved it as "topological equivalence mapping"
One kind of staircase in the world - up to homeomorphism
>>845688
very noice
