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3D graphs


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I'm not sure if this is the right section of the math area to post this but I was hoping to get some help any way. Just recently I downloaded a calculator that has the capibility to graph 3D functions which has been fun experimenting with to see what I can get to come out but to be honest I dont really understand it. I know all about 2D graphs and reading them but untill now I never had an interest in 3D so what I am asking is if sombody here could explaing how 3D graphs work, kinda like how 2D graphs use the general formula y=mx+b, but in 3D terms with an explanation. Keep in mind I am still in high school math (AP calc which Im finding now isnt that high a math to study), so if it is possible can you keep it in terms you think I might understand? Any help with this would be very appreciated thank you.

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Well, there's lots of things one can mean by a 3d graph, but I'll assume that you're going to talk about a function like z = x+y which defines some surface.

 

Basically, they're exactly the same as 2d graphs. Imagine you have some surface, and you take a cross-section through that surface (let's say this is parallel to the x-axis). Then, you effectively have some 2d graph for every value of x for one value of y. So you can build up the graph of the function by plotting lots of these curves for every value of y. That's all it effectively does.

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Well, the y=mx+b is the formula for a line in a 2-axis graph. I'm not sure what the formula for the 3-axis graph is, but like Dave said, they're just like 2d. Just follow the x, y, and z axis to plot a point (On paper) like you would with just x and y. And make sure that if it was supposed to be rectangular that it doesn't end up triangular... That sucks.

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  • 4 weeks later...

Have you ever took Linear Algebra? It teaches you vectors in 3D space and how to define them. It's a very benefical course. The most basic idea is that you plot a point following the x,y,z axis. Also, do you know the right-hand rule? It tells you which direction the x, y, or z axis is going.

 

If you have other questions, please don't hesitate to ask.

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  • 2 weeks later...

a real application(although a simple one) would be a graph showing the variation of pressure in a system with respect to temperature and volume. say the x-axis is temperature and the y-axis is volume the z axis would be pressure of course.

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