# The widest point on an ellipsoid

## Main Question or Discussion Point

I am looking for a term to describe the widest part of an ellipsoid. However this ellipsoid is irregularly shaped because it's a wine glass. As the glass goes up from the stem it continues to widen and then toward the brim it begins to narrow again just a little. So basically it is an ellipsoid which is cut off at one of the ends of it's Z-axis. I was wondering of anyone knew the name of the point where it begins to narrow again.

HallsofIvy
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there not a single point where the ellipsoid starts to "narrow" again- its a whole circle around the ellipsoid. If you write the ellipsoid in the standard form
[tex]\frac{x^2}{a^2}+ \frac{y^2}{a^2}+ \frac{z^2}{b^2}= 1[/itex]
assuming that the z axis points toward the stem of the wind glass, then the base of the bowl is at (0, 0, -b) and the bowl starts to narrow at z= 0, where the circle around the bowl is [tex]x^2+ y^2= a^2[/itex].

CRGreathouse
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HallsofIvy describes it well, but I think you're looking for a term, not an equation. I'd say it's the circle along the major axis of the spheroid (ellipse).

HallsofIvy
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The "major axis" is a line- you can't have "circle around" it. Perhaps you meant a circle in the plane perpendicular to the major axis, passing through the center of the ellipsoid.

CRGreathouse
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The "major axis" is a line- you can't have "circle around" it. Perhaps you meant a circle in the plane perpendicular to the major axis, passing through the center of the ellipsoid.
Yes, that. :)

The "major axis" is a line- you can't have "circle around" it. Perhaps you meant a circle in the plane perpendicular to the major axis, passing through the center of the ellipsoid.
In a given ellipsoid, the circle in a plane perpendicular to the major axis and passing through the center has the greatest radius. Can this circle be said to represent the equator of the ellipsoid, or does that term only apply to celestial bodies?

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You're right Ynaught, I looked it up and equator is the correct term and can be applied to more than just celestial bodies.