# Coordinates inside a ball

1. Mar 30, 2007

### bogie

A ball can be defined as the inside of a sphere. It is made up of all points inside the sphere. Is there a customary way to describe the location of points in a ball, i.e. a coordinate system to define each point?

Is there a graphics program that can be used that lets you input the coordinates and visualize the defined points graphically?

2. Mar 30, 2007

### Staff: Mentor

Either polar or cartesian coordinates, with the origin at the center would work.

3. Mar 30, 2007

### MathematicalPhysicist

yes, we call them spherical coordinates.
where do they get these names from?! (-:

4. Mar 30, 2007

### bogie

Last edited: Mar 30, 2007
5. Mar 30, 2007

### VietDao29

The equation of a sphere, having the radius R, and center (a, b, c) is:
$$(x - a) ^ 2 + (y - b) ^ 2 + (z - c) ^ 2 = R ^ 2$$
Now, a ball is a collection of the points whose distances from the center are less than or equal to R, so, the ball has the equation:
$$(x - a) ^ 2 + (y - b) ^ 2 + (z - c) ^ 2 \leq R ^ 2$$

6. Mar 30, 2007

### bogie

I found this graphic: http://mathworld.wolfram.com/SphericalCoordinates.html

It is for defining points on a sphere, but I can see how the same coordinate system would be used to define the location of points in the ball.

Are your x, y and z the same as the x axis, y axis and z axis in the graphic?

How do you’re a, b and c relate to the graphic?

7. Mar 31, 2007

### MathematicalPhysicist

(a,b,c) is the centre of the sphere, in the link youv'e given it's (0,0,0).

8. Mar 31, 2007

### VietDao29

Instead of having the center at (0, 0, 0), my sphere has its center at (a, b, c), you can look at the attachment below. Srry, if my drawing is just so bad...

The red little dot is the center having the co-ordinate (a, b, c).
The sphere is green.
Is it clearer now? :)

Last edited: Mar 31, 2007
9. Apr 2, 2007

### bogie

Yes. Your drawing is very good.

Using your drawing can you give me an example of how your formulas work, replacing the xyz and abc with numbers that relate to the drawing? Or do your formulas represent a general definition of a sphere and are not intended to describe a specific point on or in the sphere.

10. Apr 2, 2007

### robphy

11. Apr 2, 2007