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Sphere Equation Variables


Date: 08/21/2001 at 21:19:06
From: Timmy
Subject: Calculus

I'm a bit unfamiliar with the equation for a sphere and what all the 
the variables represent. In the standard equation: 

r^2 = (x-h)^2 + (y-K0^2 + (z-l)^2

...what do the points h, k, and l represent?  I'm just trying to get 
a basis for better understanding what the numbers I'm plugging in 
actually mean. 

Thanks for your time.


Date: 08/22/2001 at 13:40:18
From: Doctor Ian
Subject: Re: Calculus

Hi Timmy,

Go to one corner of a room.  The lines where the walls and the floor 
intersect are the axes of a three-dimensional coordinate system:


               z
               |
               |
               |
               +----------- y
              /
             /
            /
           x

Move h units along the x-axis; then move k units parallel to the 
y-axis; then move l (lowercase 'L') units parallel to the z axis.  
This is the center of the sphere; and r is the radius of the sphere. 

If you change the values of h, k, and l, the sphere moves around, but 
stays the same size.  If you change the value of r, the sphere grows 
or shrinks. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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