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MathGroup Archive 2005

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Re: graphing x^2+4 on x, y, and i

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61817] Re: graphing x^2+4 on x, y, and i
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Mon, 31 Oct 2005 01:17:10 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 10/30/05 at 5:49 AM, likothecat at hotmail.com (thomas) wrote:

>On Sun, 30 Oct 2005 04:55:45 +0000 (UTC), Bill Rowe
><readnewsciv at earthlink.net> wrote:

>>On 10/29/05 at 1:32 AM, likothecat at hotmail.com (thomas) wrote:

>>>Is it possible to make a 3d type of graph using the x, y, and i
>>>axes for the equation y = x ^ 2 + 4?

>>it is difficult to tell you specifically how to deal with your
>>problem. You've not defined what you mean by the "i" axis and the
>>expression you give is only dependent on two variables.

>What I mean by the i axis, is imaginary numbers.  That is, I would
>like to see the zeros at +2i and -2i as well as the parabola in x
>and y.  If that makes sense?

That helps, but it still isn't totally obvious as to what you want to show. If you want to show all solutions to y = x^2 + 4 including complex solutions, then the problem is a 4 dimensional problem. That is, if you have a complex input (2 numbers) you would have a complex output (2 numbers). 

Possibly, the package Graphics`ParametricPlot3D` will do what you want. If I regard the z-axis as imaginary and the x-y axes as real, then I could do

In[36]:=<< Graphics`ParametricPlot3D`
In[37]:=
Show[
  Block[{$DisplayFunction = Identity}, 
    {PointParametricPlot3D[{x, x^2 + 4, 0}, {x, -1, 1}], 
     PointParametricPlot3D[{0, 0, 2}, {x, -1, 1}], 
     PointParametricPlot3D[{0, 0, -2}, {x, -1, 1}]}]];

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