Drawing Quadratic Surfaces: Tips for Rendering Sheets by Hand

nameVoid
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z=y^2-x^2

Trying to render these sheets by hand is very difficult for me. I can conceptualize the sheet in general by observing that the trace in z=y^2-k^2 follows the trace of z=k^2-x^2 as z tends to negative infinity. The opposite is also true as z tends to infinity. This information combined with the hyperbolic traces gives me a general idea of the sheet. Any tips in how to draw this.
 
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You can use softwares like Maple and MatLab.
There is one online too.Check here.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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