#### DaveC426913

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A story I wrote depends on some geometry, and I want to get it straight.

Assumptions:

1] The 2D math that applies to circles and ellipses is analagous to the 3D math for spheres and ellipsoids in the ways relevant to the rest of my post.

2] An ellipse is a circle whose two foci are co-incident. Thus, a sphere is an ellipsoid whose two foci are co-incient.

What I want to figure out is what happens to the surface of an ellipse/ellipsoid when the two co-incident foci are moved apart.

Say I have a sphere of unit radius. I move its two foci two units apart. What happens to the surface?

What is the length of its semi-minor axis?

What is the length of its semi-major axis?

And, more specifically, what happens to the distance from focus-to-surface near the "ends"?

Does the distance from focus to surface decrease as the ellipsoid "stretches" thinner? (i.e. is the focus now closer to the surface than one unit?)

[ EDIT ] The correct term for my shape is a

** by magical coincidence, I am writing this

Assumptions:

1] The 2D math that applies to circles and ellipses is analagous to the 3D math for spheres and ellipsoids in the ways relevant to the rest of my post.

2] An ellipse is a circle whose two foci are co-incident. Thus, a sphere is an ellipsoid whose two foci are co-incient.

What I want to figure out is what happens to the surface of an ellipse/ellipsoid when the two co-incident foci are moved apart.

Say I have a sphere of unit radius. I move its two foci two units apart. What happens to the surface?

What is the length of its semi-minor axis?

What is the length of its semi-major axis?

And, more specifically, what happens to the distance from focus-to-surface near the "ends"?

Does the distance from focus to surface decrease as the ellipsoid "stretches" thinner? (i.e. is the focus now closer to the surface than one unit?)

[ EDIT ] The correct term for my shape is a

**prolate spheroid**- a cigar shape**. Equatorial radii a and b are the same. Polar radius c is longer.** by magical coincidence, I am writing this

*while*smoking a cigar.
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