Learning How to Sketch 3D Figures: For example: Sketch the surface z = x^2 + 2y^2

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Hckyplayer8

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Can anybody provide some good sources of how to sketch in 3D?

For example: Sketch the surface z = x^2 + 2y^2
 
Hckyplayer8 said:
Can anybody provide some good sources of how to sketch in 3D?

For example: Sketch the surface z = x^2 + 2y^2
Click to expand...
What do you mean by "sketch"?

To me, that would mean making a rough drawing by hand.

And what do you want to do with the result? That can affect the kind of drawing you need.
 
Hckyplayer8 said:
Can anybody provide some good sources of how to sketch in 3D?

For example: Sketch the surface z = x^2 + 2y^2
Click to expand...

Have you tried searching? Type "sketching 3d graphs by hand" into Google, and you should find lots of help.

Here's one place I found, in a textbook:

math.libretexts.org

1.7: Sketching Surfaces in 3d

In practice students taking multivariable calculus regularly have great difficulty visualising surfaces in three dimensions, despite the fact that we all live in three dimensions. We'll now develop …
math.libretexts.org math.libretexts.org
 
Picture the following:
Sketch z = x^2 + 2y^2
Let z=0. Draw the curve 0 = x2+2y2.
Now let z=1. Now draw 1=x2+2y2. Just understand that this graph will be on the plane z=1
Now let z=2. Now draw 2=x2+2y2. Just understand that this graph will be on the plane z= 2.
continue...
Now try to sketch the whole thing all at once (or maybe you already did that). You should get something like a bowl (it would be a bowl if the 2 wasn't there). Each graph is an ellipse. Just imaging drawing one ellipse on top of the previous one AND make each new ellipse bigger than the one before.

It takes practice but it can be done. Actually the first step is learning how to draw the x, y and z axes>
 
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