The widest point on an ellipsoid

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    Ellipsoid Point
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Discussion Overview

The discussion revolves around identifying a term for the widest part of an irregularly shaped ellipsoid, specifically in the context of a wine glass. Participants explore the geometric properties of the ellipsoid and the terminology associated with its structure.

Discussion Character

  • Conceptual clarification, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks a term for the point where the wine glass-shaped ellipsoid begins to narrow again.
  • Another participant clarifies that there is not a single point but rather a circle around the ellipsoid where it begins to narrow.
  • A participant suggests that the widest part corresponds to a circle along the major axis of the spheroid.
  • There is a discussion about the terminology, with one participant emphasizing that the "major axis" is a line and suggesting a circle in a plane perpendicular to it.
  • A later reply questions whether the circle representing the widest part can be referred to as the "equator" of the ellipsoid.
  • Another participant confirms that "equator" is an appropriate term that can apply beyond celestial bodies.

Areas of Agreement / Disagreement

Participants express differing views on the terminology and geometric properties, particularly regarding the use of "major axis" and the concept of an "equator." The discussion remains unresolved regarding the precise terminology and definitions.

Contextual Notes

Participants rely on specific geometric definitions and properties of ellipsoids, which may not be universally agreed upon. The discussion includes assumptions about the shape and orientation of the ellipsoid.

only_huce
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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.
 
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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
\frac{x^2}{a^2}+ \frac{y^2}{a^2}+ \frac{z^2}{b^2}= 1[/itex]<br /> 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 x^2+ y^2= a^2[/itex].
 
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).
 
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.
 
HallsofIvy said:
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. :)
 
HallsofIvy said:
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?
 
Last edited:
You're right Ynaught, I looked it up and equator is the correct term and can be applied to more than just celestial bodies.
 

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