# Which notation do you prefer?



## VooX (Nov 23, 2007)

I have been going through a lot of speedcubing sites for new algs. I have noticed that some things are constant in notation around the world, while others are not.

One particular notation that I have noticed popping up on a few sites has me liking it. It is the notation used for turning the entire cube.

There are two methods I have come across so far:

1) <the most common> X / Y / Z
~the letters x, y, and z are used to represent rotating the entire cube

2) <less common> (r) / (u) / (f)
~the same letters are used to represent turning the entire cube, as in turning just a single face. The difference is that when you want to denote a turn of the entire cube, the letters are put into brackets.
x=(r) y=(u) z=(f)


IMHO, the second method is the better one. Because no new letters have to be learned, it is easier to keep which side is turning straight in your head. 

As well, with the X/Y/Z method, you have to remember which side clockwise/counterclockwise are relative to. ie.- an x move turns clockwise relative to the R face not the L face.

The (r)/(u)/(f) notation method uses the same relative clockwise/counterclockwise movements as the face used in the notation.

To me the second system is easier to quickly perform without error. It is also easier to teach new cubers as they will not confuse which side is being referred to or which direction clockwise/counterclockwise is.

What do you prefer?


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## AvGalen (Nov 23, 2007)

Between those two, I would prefer the second one.

I really don't like the current notation because:
* spaces are optional (FRUR'U'F') should be written as (F R U R' U' F')
* ' is barely readable, especially in print and in high resolution screens. Why not just write it like (F R U -R -U -F) or (F R U R3 U3 F3). I like the second method best because it can also be used on puzzles like MegaMinx.
* small letters mean different things for different size puzzles (and even for scrambling and algs!)
* x y z rotations are causing a lot of confusion (until you realise xyz is like RUF)
* M E S notation is just strange (especially when you realize MES is like R'U'F')

I still think a notation that is just based on n(RUFLDBrufldb)m would be best.
n indicates the starting layers
big letters indicate single layer turns (can be slice turns)
small letters indicate multi-layer turns
m indicates the amount of "quarter" turns.

This notation could be used for any size cube, pyraminx, megaminx and maybe even other puzzles.


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## Lucas Garron (Nov 23, 2007)

AvGalen said:


> * M E S notation is just strange (especially when you realize MES is like R'U'F')


You mean R'U'F ?
One more thing:'s are hard to use with apostrophes and quotes. As in "'RU'R'''s last turn."

EDIT: Also, I don't like using parentheses for anything but grouping. We don't want even more inconsistency unless we find a uinform consensus and switch together.


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## VooX (Nov 23, 2007)

AvGalen said:


> * M E S notation is just strange (especially when you realize MES is like R'U'F)



Don't even get me started on how confusing MES is to keep straight in my head!


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## hdskull (Nov 24, 2007)

I like the 2nd one also because it proves to be less confusing, and as far as I know, Japanese/other Asian cubers use it. I think it's a lot less confusing for beginners and also, the people who use that also use Fw/Uw/Rw/Lw; which I also think is much less confusing.


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## Johannes91 (Nov 24, 2007)

The second notation is used mostly by Japanese cubers. Multiple rotations are combined like (u f).



AvGalen said:


> ' is barely readable, especially in print and in high resolution screens.


Use better fonts. I don't have any problems seeing it, even though I use quite high resolution.



AvGalen said:


> Why not just write ... (F R U R3 U3 F3).


Because it's not three times clockwise, it's once counter-clockwise. Counting U3 as 1 QTM doesn't seem intuitive at all.



AvGalen said:


> ... it can also be used on puzzles like MegaMinx.


And so can '.


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## Pedro (Nov 24, 2007)

AvGalen said:


> * small letters mean different things for different size puzzles (and even for scrambling and algs!)



why?

as far as I know, r means "the two right layers", no matter if it is a 3x3 or a 7x7...(in WCA scrambling)

and people use r for "just the second layer from the right" as they're lazy to write rR'...(mostly in bld algs/tutorials)


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## Lucas Garron (Nov 24, 2007)

Pedro said:


> AvGalen said:
> 
> 
> > * small letters mean different things for different size puzzles (and even for scrambling and algs!)
> ...



Okay, you go execute: R(r'R)(uU')(rR')U(r'R)(u'U)(rR')U'R'
And some people would write that as Rr'RU'urR'Ur'RUu'R'rU'R'.
Laziness is not the issue compared to legibility and accuracy.

I used to like the idea of it always meaning "two layers," but it's much less convenient. Also, a lot of scramblers for 4x4x4 give something like Rud'l', which is clearly redundant in a double-turn system. This is a fun issue when you're using the same scrambles to race someone online...


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## Pedro (Nov 24, 2007)

Lucas Garron said:


> Pedro said:
> 
> 
> > AvGalen said:
> ...



yeah, maybe it's not lazyness...but...

I never had something like that on the WCA scrambler...on JNetCube you get it, as it was built when r meant just the 2nd layer from the right...

what would be the best way? :confused:

something like 1R, 2R, 3R could work, meaning 1st from the right, 2nd from the right, and so on...

but how would our current r be? 12R?


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## Raltenbach (Jan 26, 2008)

Sorry to revive such an old thread for this, but I couldn't find an answer for this anywhere (even in the other notation threads): Could someone please explain x y z and x' y' z' turns. I've seen a lot of inconsistency on this. I' learning PLL and it seems some cases require cube rotations(F perm for example). Having to ask this question at all shows the benefit of the second method (totally intuitive).


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## Pedro (Jan 26, 2008)

Raltenbach said:


> Sorry to revive such an old thread for this, but I couldn't find an answer for this anywhere (even in the other notation threads): Could someone please explain x y z and x' y' z' turns. I've seen a lot of inconsistency on this. I' learning PLL and it seems some cases require cube rotations(F perm for example). Having to ask this question at all shows the benefit of the second method (totally intuitive).



x = turning the whole cube as R
x = R'

y = turning the cube as U

z = turning the cube as F


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## alltooamorous (Jan 26, 2008)

Raltenbach said:


> Sorry to revive such an old thread for this, but I couldn't find an answer for this anywhere (even in the other notation threads): Could someone please explain x y z and x' y' z' turns. I've seen a lot of inconsistency on this. I' learning PLL and it seems some cases require cube rotations(F perm for example). Having to ask this question at all shows the benefit of the second method (totally intuitive).



Thanks so much for reviving this thread. I saw it, and wow I know can actually memorize what X Y and Z mean.


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## Raltenbach (Jan 26, 2008)

Pedro said:


> x = turning the whole cube as R
> x = R'
> 
> y = turning the cube as U
> ...



Okay, this is a perfect example of why this is confusing to me. Here you write that x is turning as R, but then say x is like R'. Which one is it? If you could please notate it as what regular quarter turn it moves like I'd greatly appreciate it.


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## TimMc (Jan 26, 2008)

I don't quite understand the poll.

There are several different notations for cubing which aren't listed in the poll. The given options just seem to be a subset of a few forms of notation... ?

Tim.


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## Pedro (Jan 26, 2008)

Raltenbach said:


> Pedro said:
> 
> 
> > x = turning the whole cube as R
> ...



sorry, x' = R'


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## alexc (Jan 26, 2008)

I learned using xyz, so I don't mind it that much.


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## Lucas Garron (Jan 26, 2008)

I only avoid (r) and so for consistency. Redundant, optional, separate, or fingertrick moves are often offset with parentheses only as a grouper.

What does this mean?
(r)(Ur')(U')(r'F)(r2U')(r')(U'r)(Ur')(F')


I have an ingenious solution, though!
You know how mathematicians use Greek letters for angles and rotations?
We should, too!
υ ρ φ λ β δ

Even better, we have another set of characters!
Υ Ρ Φ Λ Β Δ

We can use one set for rotations, and another for slices, and leave the lowercases for something double-layer! It even generalizes nicely to 4x4x4 and 5x5x5 [spacing]! We just need to avoid B


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## qqwref (Jan 27, 2008)

Well, here's a system that might look odd but is definitely unambiguous and easy to read. I tried to modify the system I usually use a bit, to make it even easier to use.

If n is any integer, nR signifies the slice that is n layers from the R face. Also, nr signifies all layers UP TO the slice that nR signifies. So M and 2R are the same slice on a 3x3x3. To write turns, instead of just putting the slice, you have to add the direction yourself. 1R is a slice, 1R+ or 1R- is a turn. + is clockwise and - is counterclockwise; for a double turn you would write 1R+2 or 1R-2. Note that the 2 is at the end; this is because 2 at the end of something just means to do that action 2 times, like (1R+ 1U-)2. Note that spacing is not absolutely necessary for this notation, but definitely suggested. For cube rotations, use cR (c looks different from any numeral and stands for "cube").

So a standard sune would be written 1R+ 1U+ 1R- 1U+ 1R+ 1U+2 1R-.

Well, sure, it does take up a lot of space (you can write R for 1R if you want, and r for 2r)... but it's definitely unambiguous.


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## abbracadiabra (Jan 27, 2008)

So how would you represent a clockwise turn of the left face? Would it be 3R+, 3R-, or 1L+?


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## qqwref (Jan 27, 2008)

You could always write 3R- if you want, but 1L+ would be much better. For the NxNxN cubes the sides are FURDBL like always. If you're doing a more complicated puzzle you could define the sides to be any letter or group of letters - for example you might want a BR side on the megminx, and you could still write 1BR+ without confusion.


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## brad711 (Jan 28, 2008)

Its easier to remember with (r) or (u) or whatever.


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## qqwref (Apr 4, 2008)

I still don't know what you intend to do with something like (r u'). Is that a cube rotation or a fingertrick of double-layer turns only? Clearly you can't have both lowercase letters for turns and lowercase letters for cube rotations at the same time. As much as x, y, z is confusing to some I don't think this notation is any better, and in fact it is more confusing in the long run because parentheses now have multiple meanings.

And I never understood the value of Rw. It takes up much more space, isn't intuitive or expandable to bigger cubes (if you are going to use a letter it should stand for double layer or something like that, emphasizing the double), and also makes slice turns very long to write, something like (RwR').


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## brunson (Apr 4, 2008)

I keep the straight using the "left hand curl" rule. 

Anyone who's taken physics is probably familiar with Fleming's "right hand rule" for induced electromagnetic fields. You take your right hand, stick your thumb out and allow your fingers curl around like you'd hold a can of Red Bull. If current is flowing through a conductor in the direction your thumb your thumb is pointing, then the induced magnetic field flows around the wire in the direction your fingers would wrap around it. See: http://www.diracdelta.co.uk/science/source/f/l/flemings right hand rule/source.html

The x/y/z rotations conform to a left hand rule. If you're used to drawing Cartesian coordinate graphs, then the x axis on a piece of paper would be horizontal, increasing positively away from zero to the right, the y axis would be vertical, increasing in the up direction and the z axis would come out of the paper towards your face. If you hold your left hand as described above and point your finger in the direction of the axis in question, a regular turn is in the direction your fingers curl and a ' twist is the other way.

That's how I kept it straight in my mind before it became natural to me, so if it makes sense and is useful to you, you're welcome to refer to it as "Brunson's left hand rule of cube rotations".

Thank you very much, I'll be here all week.


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## qqwref (Apr 4, 2008)

Well I'm going to admit that I know them more by what they are associated with than anything else. y is the cube rotation I use a lot for F2L, and x is the nice easy one you use to do fingertricks on B and F. Once I saw those associations it was always pretty easy for me to know which is which.


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## dChan (Apr 4, 2008)

x, y, and z. Not that they are easier; it is just that I learned notation that way from Macky's site. Plus I always just imagine a graph with a 3D line sticking through(for z) and when I do that it is very easy to figure out what to do.


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## pcwiz (Apr 4, 2008)

brunson said:


> The x/y/z rotations conform to a left hand rule. If you're used to drawing Cartesian coordinate graphs, then the x axis on a piece of paper would be horizontal, increasing positively away from zero to the right, the y axis would be vertical, increasing in the up direction and the z axis would come out of the paper towards your face. If you hold your left hand as described above and point your finger in the direction of the axis in question, a regular turn is in the direction your fingers curl and a ' twist is the other way.



Oh yes! Comparing these x, y, and z rotations to the Cartesian coordinate graphs is a really easy way to remember this! Thanks a lot! I don't understand what you're trying to say for the other things but the Cartesian coordinate is great!

If you know what the Cartesian coordinate is but don't know how to use it with your cube rotations, here's another explanation. In the Cartesian Coordinate system, the x axis runs in a horizontal line (runs through the center of the left and right faces). So a x turn would be turning the cube around the imaginary horizontal line running through the center of your cube in a clockwise direction. In the coordinate system, the y axis runs vertically (an imaginary line running through the up and down faces). So, thinking that an imaginary line runs through your center of your cube vertically, rotate your cube around that line in a clockwise direction to get y. Lastly, the z axis is an imaginary line that runs through the center of the front and back faces of your cube (I don't know how to explain it like horizontally or vertically.) Then, you rotate your cube around the z axis in a clockwise direction to get z.

If you understand the Cartesian Coordinate system, remembering which way to turn the cube during the cube rotations is SUPER easy. If you don't, I'm sorry, you'll just have to remember that..

x = turning the whole cube R
Y = turning the whole cube U
z = turning the whole cube F


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## fanwuq (Apr 4, 2008)

I like qqwref, lucasgarron, and avgalen's ideas. 
I too have thought about it and arrived at something similar to avgalen's.
I hate the right hand rule for physics! 
I find xyz very intuitive. I understood how to turn them as soon as I figured out that they are whole cube turns. I confused (r) as an optional double layer r at first. But now I can read both well.
i do hate the inconsistencies between puzzles. especially r can be double layer for 3x3 yet be inner for big cubes and tips for pyraminx.


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## dChan (Apr 4, 2008)

I think for the 3x3x3, an extra "w" at the end of a notation is best for signifying double layer turns. It conforms better to the whole line of notations for the other puzzles.

It is also easy to understand. Whenever I see, for example, Rw, I say to myself, "R-wide" which tells me to turn two layers because two layers are "wide."


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## pcwiz (Apr 4, 2008)

Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.


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## qqwref (Apr 4, 2008)

dChan said:


> It is also easy to understand. Whenever I see, for example, Rw, I say to myself, "R-wide" which tells me to turn two layers because two layers are "wide."


Two layers might be wide for a 3x3, but as I said the notation doesn't work for anything bigger. Two isn't that wide for a 4x4 (isn't 3 layers wider?) and it certainly doesn't cut it on a 7x7.

I hope you will all support me at this new notation I just came up with, for large cubes. It covers every possible move for cubes up to 7x7.
Rxs - one layer (R extra shallow)
Rs - two layers (R shallow)
Rm - three layers (R medium)
Rw - four layers (R wide)
Rxw - five layers (R extra wide)
Rxxw - six layers (R extra extra wide)
You can't get any more intuitive than that. It works just like clothing sizes, which everyone is already familiar with. Everyone should start using this method immediately. I suggest we all make a formal request to the WCA to adopt it. (Or maybe you see my point. Also, it's cumbersome.)



pcwiz said:


> Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.


Funny, despite being a math major at Caltech, I've never heard of it. Do you think you could elaborate a bit more? It sounds interesting.


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## Lucas Garron (Apr 4, 2008)

Even better:

Single-layer: Ri
Double: Rii
Triple: Riii
Quadruple: Riv
Quintuple: Rv
...



Actually, it's not THAT bad, and obvious to generalize. Now we just have to get w compatible with i.


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## qqwref (Apr 4, 2008)

No, I have an even more intuitive system. Forget block turns entirely. Let's just write everything in base 4 notation (1 meaning clockwise) on the R, U, and F axes.

So what's now an Rr move on the 4x4x4 would become R0011. l becomes R0300. An lr antislice move becomes R0310. What is now a y rotation simply becomes U1111. This is clearly a superior notation to all others, since it requires no interpretation whatsoever and no special terms have to be memorized, except for R, U, and F. The size of the cube is also immediately implied in the number of base-4 digits used. If you do not adapt THIS new terminology you will be assimilated by the Borg anyway. Resistance is futile.


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## blade740 (Apr 4, 2008)

I myself think we need a more beautiful and artistic notation system. I propose the use of colors. 

R Is the outermost layen on the right.
RRR Would be the 3 rightmost layers
RRRRRR Is the2nd-7th rightmost layers.


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## pcwiz (Apr 4, 2008)

qqwref said:


> pcwiz said:
> 
> 
> > Does anybody here know what the Cartesian Coordinate system is besides Brunson? Because I think it's an excellent way to remember which way to turn the cube.
> ...



I don't think the Cartesian Coordinate system is used in math...

I learned it in school like two weeks ago and I'm not exactly sure what it's used for... I just learned what it was and... I don't know.. I learned it when I was learning about robots so... Nevertheless, I know what it is, and if you compare it to the x, y, and z turns of the Rubik's Cube, they are exactly the same. Therefore, if you know what the Cartesian Coordinate system, is, you'll immediately know which direction to turn the cube with the x, y, and z notation.

I'm sorry I didn't explain it because it's hard to explain and I don't know what it's used for. So I myself am not too familiar with the topic so I wouldn't really be able to teach you. Sorry! Maybe you can ask Brunson?


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## Jai (Apr 4, 2008)

blade740 said:


> I myself think we need a more beautiful and artistic notation system. I propose the use of colors.
> 
> R Is the outermost layen on the right.
> RRR Would be the 3 rightmost layers
> RRRRRR Is the2nd-7th rightmost layers.


Yes, this idea would work PERFECTLY , especially for colorblind people/ people with color recognition problems (like Harris), and for people with monochrome printers.  Imagine doing team BLD with that.. 
"RED BLUE ORANGE GREEN YELLOW!"
"Whoa, slow down there.."
"Oh,no, sorry, I just lost my pencil crayons."


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## brunson (Apr 4, 2008)

pcwiz said:


> qqwref said:
> 
> 
> > pcwiz said:
> ...


I'm pretty sure qqwref is being facetious, but I can't quite tell if you are or not.


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## pcwiz (Apr 4, 2008)

brunson said:


> pcwiz said:
> 
> 
> > qqwref said:
> ...




Wait what? I had to look in the dictionary to understand what "facetious" means. So you mean he's being sarcastic or I'm being sarcastic? I'm confused! :confused: Anyway, I don't know what you mean by this post but I'm being serious and I'm not really sure if it's used in math so...


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## Cubie Newbie (Apr 4, 2008)

The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry. 

You can extend this system into any dimension. In 3D, the x axis is horizontal, the y axis points toward you, and the z axis is vertical. Now, I'm not going to philosophy about Tetraspace, aka (w,x,y,z,) coordinates.


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## pcwiz (Apr 4, 2008)

Cubie Newbie said:


> The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry.
> 
> You can extend this system into any dimension. In 3D, the x axis is horizontal, the y axis points toward you, and the z axis is vertical. Now, I'm not going to philosophy about Tetraspace, aka (w,x,y,z,) coordinates.



You made some errors.

x = horizontal axis 
y = vertical axis
z = pointing towards you

You don't use z in ordered pairs or do you?:confused:


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## Lucas Garron (Apr 5, 2008)

pcwiz said:


> Cubie Newbie said:
> 
> 
> > The Cartesian Coordinate system, according to Wikipedia, is basically your normal (x,y) system using ordered pairs. All of you should have learned this in elementary school in geometry.
> ...



You also made some errors.

1) x is not any less horizontal than what you call z.
2) z is not pointing towards "you," by most conventions of z-depth I've seen, which make z away from you. (Same applies to Cubie Newbie's y-axis.)
3) Both of you are equally wrong and right. y and z doen't inherently point in a direction, it's whatever you define it as (most orthogonal conventions have x the same way).

See Wikipedia and MathWorld.

1) He did not use z in an ordered pair, but in an ordered quadruple (which I presume contains a typo extra comma).
2) I don't know if he does. But if he does, so? He can use (rubiks, cube) for coordinates if he wants!
(Who's up for rubik geometry? rubiks²+cube²=1  )

Cubie Newbie: Why "philosophy"?


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## pcwiz (Apr 5, 2008)

Okay then how would you explain the Cartesian Coordinate system?


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## blade740 (Apr 5, 2008)

The cartesian coordinate system is the most commonly used today. You measure distance away from an origin in each dimension. It can be 1-dimensional, 2-dimensional, 3-dimensional, 19872-dimensional. If you're using (x, y) you're using the cartesian system. If you're using (x, y, z) you're using it. It's just an extra dimension.


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## pcwiz (Apr 5, 2008)

blade740 said:


> The cartesian coordinate system is the most commonly used today. You measure distance away from an origin in each dimension. It can be 1-dimensional, 2-dimensional, 3-dimensional, 19872-dimensional. If you're using (x, y) you're using the cartesian system. If you're using (x, y, z) you're using it. It's just an extra dimension.



So how would you explain it to a person who has no idea what the Cartesian Coordinate system is and doesn't know what it's for?


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## brunson (Apr 5, 2008)

pcwiz said:


> So how would you explain it to a person who has no idea what the Cartesian Coordinate system is and doesn't know what it's for?



Well, first I'd ask if they've ever graphed anything or seen graph paper, but since there are people on the list that my not have done that I'll take this approach:

Look at a wall in the room your in. Pick one that, while you're facing it, meets the floor and another wall in the lower left hand corner, I'm going to refer to this corner as the "origin". Now, spit on the wall. Where did the spit land?

There are a few simple ways you can describe where your spit landed. Let's say you drew a line straight down from the loogie to the floor and another one horizontally to both walls. Now if you were to take a tape measure and measure the distance along the floor from the origin to the vertical line you drew, then a second measurement from the origin straight up to the horizontal line, you could say, 5 feet horizontally and 4 feet vertically from the origin. The uniquely identifies where the spit is on the wall.

Hey, guess what? You've just used two dimensional Cartesian coordinate to describe where you hocked your phlegm.  If you were to lay out a grid on that wall drawing a vertical line every foot from the origin and a horizontal line every foot from the floor, that would be a two dimensional coordinate system. 

Rene Descarte, the French philosopher and mathematician, was the first to formalize this system of describing location. The corner formed by the wall and the other wall to the left, he designated the y axis and the corner formed with the wall and the floor he called the x axis. So, if you spit again you only have to say, "It landed at (4,6)" to describe the location 4 feet from the left wall and 6 feet from the floor.

This can be extended to 3 dimensions by adding an additional axis along the floor and the wall to the left, and we'll call that... the z axis! So, standing in the middle of room you can describe the location of your head as 4 feet from the wall on the left, 5 feet off the floor and 5 feet from the front wall (measured along the z axis) or (4, 5, 5) in three dimensional space. Notice that our concept of two or three dimensions is a direct derivative of the Cartesian coordinate system.

So, an excellent model of this is the core of your 3x3x3. Take your cube apart right now because you know it's been too long since you cleaned it. Look at the core, it has six arms extending from the center. Think of the center of the cube as the origin, the horizontal arms pointing left and right are the X axis, the vertical arms as the Y and the ones pointing towards and away from you are the Z axis. An x rotation of the cube turns it around the x axis, similarly with y and z rotations, they turn the cube around the y and z axes.

Now the only question is which way to turn it. That's where the left hand rule come in. In a standard cartesian system with your origin in the lower left hand corner of your room the origin it 0,0,0 and x increases positively towards the right and negatively towards the left, y grows up and z grows as it comes towards you.  

So, if you take your left hand as described in my previous post and point your thumb in the direction that x gets larger, i.e. to the right, then your fingers curve down and away from you. Turning the top face of the cube away from you and down is a positive x rotation, turning it the other way is a negative x rotation, or an x' turn. The same with y, pointing your thumb up your fingers turn away and to the right, so a cube rotation in that direction is y and the opposite is y'. Z rotations work the same way, just point your thumb at your face and a clockwise rotation, just like your fingers curl, is z and counter clockwise is z'.

So there you have your first two weeks of Algebra 2 summed up in a single posting. You can paypal me a dollar for the education. ;-)

Seriously, though, I hope that was clear and helpful.


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## fanwuq (Apr 5, 2008)

Pcwiz, 

I thought your were sarcastic! I mean, everyone should know what the Cartesian coordinates are. What are in? 3rd grade? That is why x,y,z is so much easier to understand.

(r) (u) (f) are ambiguous. I thought they are optional or fingertricks for double layer turns.

I do like 001 for R, but it is too long to right. I say the current system has it's faults but is understandable in general. We do need a new system when the 6x6+ Vcubes come out however.


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## Feanaro (Apr 6, 2008)

I have never even seen the second kind of notation. Do the ()'s make a r different than a (r)?


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## MistArts (Apr 6, 2008)

Feanaro said:


> I have never even seen the second kind of notation. Do the ()'s make a r different than a (r)?




Yes... *r* is a double layer turn and *(r)* is an *x* rotation


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## Feanaro (Apr 6, 2008)

Wow, that is a lot easier. I also never connected the x,y,z notations to the cartesian plane. 

*3x3x3 PB: 18.22 sec
3x3x3 OH: 1:17
3x3x3 BLND: 2:55
2x2x2 PB: 7.35
4x4x4 PB: 2:30*


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## pcwiz (Apr 6, 2008)

brunson said:


> pcwiz said:
> 
> 
> > So how would you explain it to a person who has no idea what the Cartesian Coordinate system is and doesn't know what it's for?
> ...



Great Description! I can easily understand it and I think a beginner would too!


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## pcwiz (Apr 6, 2008)

fanwuq said:


> Pcwiz,
> 
> I thought your were sarcastic! I mean, everyone should know what the Cartesian coordinates are. What are in? 3rd grade? That is why x,y,z is so much easier to understand.



Well I'm just saying because I didn't learn it in 3rd grade (at least not the z axis) and nobody here mentioned it except Brunson. I never knew the simple ordered pairs was the *Cartesian* coordinate system. I just thought it was the coordinate system.

By the way I'm not sarcastic a lot, and if I tried, it would be the worst sarcasm you've ever seen.


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## pcharles93 (Apr 6, 2008)

Wait, why is the "Cartesian" necessary? If it's the only coordinate system out there, why label it with an unnecessary adjective?


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## pcwiz (Apr 6, 2008)

Maybe the person who invented the Cartesian Coordinate system has the last name of Cartesian, and the want to be credited for their invention?

This is just a logical guess.


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## blade740 (Apr 6, 2008)

It's not the only coordinate system out there. It's just the most commonly used. The spherical system comes to mind. (r, θ, φ)


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## brunson (Apr 6, 2008)

It was named after Rene Descarte and there are other coordinate systems.


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