#1
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Simple math plotting question
So this is extremely simple, but I don't have the literature to read up on and it seems hard to find this question by googling. So sorry if it's too simple!
Say we have a function z which depends on 2 variables, x and y (say z=x-y for the sake of.. something) If we would like to plot this we would get 3 dimensions, x y and z. What if me make, for example x, exogenous? Would we still want to plot this in 3 dimensions? It should be possible to plot it in 2 dimensions yes? But what is the mathematically "correct" way to do it? Instinctively I'd still figure there will be 3 dimensions where there . But if it's not, do we just view x (in this case) as a constant in a 2d plot like z=c+y? So when x varies it only changes the intercept of the z axis? Sorry again since this is ridiculously simple.. Thanks! |
#2
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Re: Simple math plotting question
If I understand your question correctly, you can start by considering it in the 2D case. These represent the cross sections of the 3D graph. So in the example of z=c+y, with c a constant, then in the 2D graph that would obviously be a line of slope 1 with z-intercept of c. Since x does not affect this graph, these types of cross sections will always be the same. So in a sense, you are taking the 2D case and sliding it through all possible values of x, in this case resulting in a plane in 3-space.
If you instead had, for example, y^2 + z^2 = 1, then the cross sections are circles of radius 1 centered at the origin, but this occurs for all values of x, so the result is a cylinder. I hope that made sense/answered your question. |
#3
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Re: Simple math plotting question
Aah ya that makes sense.
So I will still be plotting this in a 3 dimensional space, and will have the same zy plane for all x then yes? So graphically this would look like a linear plane with a constant slope going through all x? Thanks a lot mickey! |
#4
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Re: Simple math plotting question
Sorry for bringing this back up..
Does anyone know a good plotting program where you can assign exogenous variable and stuff so I can get a good feel for how this works? I'm still a bit confused how, for example, a z=x^2+y with 'normal' variables graph differs from a z=x^2+y with x as an exogenous variable. |
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