Visualizing a strange quadric surface

  • Thread starter Woland
  • Start date
18
0
Hi all,

I am trying to visualize the following quadric surface:
x^2 + y^2 + z^2 = z

Could someone please help me understand what this surface looks like? I could not find an example of this one on the internet.

Thank you.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
Do some algebra to simplify it. (e.g. things like collecting similar terms, completing the square, factoring, change of variable, etc)
 
654
3
Consider what the surface
(x-a)^2 + (y-b)^2 + (z-c)^2 = d

looks like
 
18
0
(x-a)^2 + (y-b)^2 + (z-c)^2 = d is a sphere centered at a, b, c with radius square root of d.

Now regarding the first post, I can bring the z over to the left hand side:

x^2 + y^2 + z^2 - z = 0

Then complete the square

x^2 + y^2 + (z - 1/2)^2 -1/4 = 0
[(z - 1/2)^2 = z^2 - 2*1/2 z + 1/4]

Then

x^2 + y^2 + (z-1/2)^2 = 1/4

This means that this is a sphere centered at 0,0, 1/2. Is that correct?
 

mathman

Science Advisor
7,668
383
This means that this is a sphere centered at 0,0, 1/2. Is that correct?
Yes and the radius is 1/2.
 

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