What is the fucking point of Cartesian coordinates?

I don't understand what this smug motherfucker thought when he created this shit math that I don't think has any application to the real world. Is Cartesian coordinates used for anything else besides school taught mathematics?

Rolling papers

Are you serious?

>Is Cartesian coordinates used for anything else besides school taught mathematics?

Are you in elementary school or something?

Cartesian coordinates are used everywhere

>Is Cartesian coordinates used for anything else besides school taught mathematics?
Yes. In every single engineering field.

>Are you in elementary school or something?
No, I've graduated highschool but I don't see how this type of math can be used in any other modes outside of school.

Forgive me if I am ignorant but it just seems like something only used in school.

Is it really that important?

It makes solving many basic physics problems much, much easier. So yes, it is.

Yes it is used everywhere in physics, and thus by extension it is used everywhere in engineering.

You won't use it..

But someone who is smart might.

I too read SMBC

you guys must be new to Veeky Forums

OP's filename is triggering me
>triggering my D

sorry that's the best I got.

Actually in most real world problems it's easier to transform from cartesian coordinates to spherical. Even cylindrical is better than cartesian.

I'm pretty curious here, what's Veeky Forums's favorite coordinate system?

I just choose elements from normal subalgebras and quotient algebras.

>he doesn't define new coordinate systems as needed
Get a load of this Newtonian Pleb

I prefer polar coordinates because it looks cool

Are you saying we dumb people don't use Cartesian coordinates?

Who do you think you are? Stephen Hawkings?

>I've never needed to read a graph in my life

I think you should reread global rule 2.

Nice bait

6/10

I'm 21, you ain't got nothing on me.

If it were bait, it would have exponentially more replies than this. Probably 152 if it were truly a 6/10 bait.

ITT: Some butt-hurt undergrad who can't into cartesian

Cartesian coordinates are important and "natural" because they exhibit objects as being the product of two other objects. The coordinates are really encoding the projections of the space onto the two axes, which is the characterizing structure of a product. Other coordinate systems, such as polar coordinates, don't supply the structure necessary to characterize the plane as a product, as in this example the origin causes problems (specifically because (0,a)=(0,b) for all a and b, so a function into the plane and projected from these coordinates fails to specify two unique functions to the circle and the half-open line). Furthermore, for Euclidean space cartesian coordinates are the only ones exhibiting this property, up to isomorphism. This owes to the deep combinatorics that arise in K-theory, but I think the result can be proved using a simple Eilenberg swindle as well.

lol the cartesian plane pretty much pushed the connection between algebra and geometry, so much that the graph of a function is a well defined set theoretic construct nowadays. It is that useful.

>basic physics and motion in 2 dimensions
>no Cartesian coordinates
Pick one.

Not to mention ordered pairs (and other ordered n-tuples) as well as the notion of a cross product are both used throughout math. In fact even the most basic algebraic operations of standard addition and multiplication on the integers are formalized using ordered pairs.
E.g. we have +: N x N ---> N

For small scale experiments, the earth might as well be flat. Only some of the biggest structures need to take the earth's curvature in account. Also, crystal lattices

Basic computer graphics? Pixel grids?

>google this thinking it is some really complex bullshit
>lol no literally just 3rd grade coordinate x and y graph shit

LOL ITS FUNNY BECAUSE IT SOUNDS LIKE LE SUPER EPIC HARD CALCULUS LOLOLOLOL

NIGGER

Did you really have to google Cartesian coordinates?

What in the actual fuck?

Underage reported

Dude... "Cartesian coordinates" does not sound like super hard calculus

Impossible that you're not underage. Everybody and everything I know refers to this "3rd grade coordinate x and y graph shit" as the "Cartesian coordinate system."
>inb4 haha I was pretending to be retard Xdd

Here they are literally just called coordinates and other systems are specified

And what do they called the Cartesian product of two sets over "there"? Or the Cartesian closed category? Its obvious that the highest level math class you've ever taken is probably like Calc I-III, if that. Not that that's a badd thing, but you shouldn't be acting condescending about someone's usage of the phrase "Cartesian coordinates", especially when that's standard terminology.

I'm not the guy 3 people replied to. I just said that cartesian coordinates are called just coordinates here. Cartesian product is a cartesian product.

I was explaining how/why we graph things to my brother and realized that the points are projections of numbers.

There are ramifications for this, but I dont know what they are.

I'm in a graphics class right now and coordinates are pretty fucking important for that class.

Well, it's more the other way around: the numbers are projections of the points. You can project onto any given coordinate to get a number, losing information on the other coordinates. It's a very important concept, though, and you are right that it has ramifications! For one, general functions can be abstractly defined as sections to a product projection. Meaning, a function from A to B is a map that sends every element in A to one of the "coordinate fibres" over it (imagine the line x=c for some constant). Intuitively, this is just saying that every point in the domain gets sent to a unique point in the codomain, as fibres don't overlap.

Well, what happens when you put the coordinate plane onto some other shape, so that the projection intersects with itself?

How do you know about the information from these new points? Do coordinate fibres and vector bundles have anything in common?

I was specifically talking about Euclidean space with Cartesian coordinates. General manifolds are (special cases of) sheaves on the Cartesian site. What this means is that a manifold is covered by coordinate charts, and is locally Euclidean. Single charts may fail to extend over the entire space, but you can always slide your coordinates around consistently. We only really need the local coordinates because of this. As you have noticed, though, we cannot express a general manifold as a product of simpler spaces. This is why manifolds are so useful, though, because we can get interesting global structure despite the rather boring (but well-behaved) local structure.

not him, but
>outside of school
>give an example in school

So a lot of things are just general cases of more simple things right?

Ive been trying to figure out what a sheave is, intuitively. I think better geometrically than algebraically

Sheaves are intuitively just the global gluing together of a bunch of local bits of information, which are the objects of the site of definition. The gluing is mediated by the gluing axiom on sheaves, which says that the local piece on the intersection of two abstract charts is compatible with the data on those charts. For manifolds, it says that you get a diffeomorphism on where charts overlap. It lets us not only see the global object as glued together from local pieces, but also transition between local pieces freely.

Legend has it that Descartes was staring at a tiled ceiling and want the describe how far a fly was from each of the edges.

How would you describe a fly's position, if not taking some sort of measurements from the edges of the ceiling?

This is what popped into my head the, sheaves are the circles. Im just trying to make this make sense to me.

Lol, oops

While you actually could devise some useful notion of sheaf on circles by using a site of infinitesimally thickened circles, manifolds are sheaves by their local patches. I can't post an image of it right now, but imagine how you can build a sphere by gluing together two disks along their boundaries. Each disk is a chart, and the boundary is where they overlap. Technically, extra care must be used in this example, but this paints the picture.