- #1
mesa
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How would you graph a square of any dimension on the cartesian coordinate system?
chiro said:Hey mesa.
What exactly do you mean? Do you mean instead of representing x you represent x2 for a particular vector (where x is the 1st element of the vector)?
Mentallic said:Maybe mesa means an actual square (quadrilateral)?
chiro said:Ohh I see what you're saying now.
It depends on the number of dimensions and the particular attribute you are trying to visualize.
Typically what happens in high-dimensional spaces, is that a specific kind of projection is used to create a visual of that attribute in a two or three dimensional space.
The short answer is that it depends on the attribute you are trying to visualize, but the kinds of things would most likely be similar if not equivalent to the ones used in a normal cartesian geometry. (It's hard to give specifics without specifics).
mesa said:Basically I am looking for (an)other function(s) that will result in a graph of a plain old square on a two dimensional cartesian coordinate system.
LCKurtz said:##|x|+|y|=1##
##max \{ |x|,|y|\} = 1##
mesa said:That's a nice solution, and takes care of the domain/range problems I was having.
Got anything else?
LCKurtz said:You can rotate and translate it to anywhere and resize it by changing the 1:$$
|(x-a)\cos(\alpha)-(y-b)\sin(\alpha)|+|(x-a)\sin(\alpha)+(y-b)\cos(\alpha)| = 1$$
Isn't there a problem at x=0 or am I missing something?acabus said:[tex]|x+y|-|x-y| = 1[/tex]
acabus said:[tex]|x+y|-|x-y| = 1[/tex]
mesa said:Isn't there a problem at x=0 or am I missing something?
LCKurtz said:That's just a typo, he means ##|x+y|+|x-y|=1##. Same as my first one but squared up with the axes.
To plot a shape on the cartesian coordinate system, you will need to have the coordinates of the shape's vertices. Start by labeling the x and y axes and then plot each point based on its x and y values. Once all points are plotted, connect them in order to form the shape.
The cartesian coordinate system is used to graphically represent relationships between two variables. It allows for easy visualization of data and can help identify patterns and trends.
The horizontal axis is labeled as the x-axis and the vertical axis is labeled as the y-axis. The origin, where the two axes intersect, is labeled as (0,0). The positive direction on the x-axis is to the right and the positive direction on the y-axis is upwards.
Yes, a shape can be graphed on the cartesian coordinate system using any number of quadrants. Some shapes may only have points in one quadrant, while others may have points in multiple quadrants.
To determine the coordinates of a point on the cartesian coordinate system, you will need to know its distance from the origin in the horizontal direction (x-axis) and then in the vertical direction (y-axis). The coordinates are written in the format (x,y), with the x-coordinate always written first.