The widest point on an ellipsoid

In summary, the conversation discusses the term for the widest part of an irregularly shaped ellipsoid, which is a wine glass in this case. While there is not a single point where the ellipsoid starts to "narrow" again, it can be described as a circle around the major axis in the plane perpendicular to it and passing through the center. This circle can be referred to as the equator of the ellipsoid, a term that can be applied to more than just celestial bodies.
  • #1
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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  • #2
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].
 
  • #3
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).
 
  • #4
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.
 
  • #5
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. :)
 
  • #6
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?
 
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  • #7
You're right Ynaught, I looked it up and equator is the correct term and can be applied to more than just celestial bodies.
 

1. What is an ellipsoid?

An ellipsoid is a three-dimensional geometric shape that resembles a stretched or flattened sphere. It is defined by three axes, with one axis being the longest and the other two being equal in length.

2. How is the widest point on an ellipsoid measured?

The widest point on an ellipsoid is typically measured by finding the distance between two opposite points on the surface of the ellipsoid, also known as the major axis. This distance is known as the equatorial diameter.

3. What factors affect the width of an ellipsoid?

The width of an ellipsoid is affected by its three axes, which can vary in length and orientation. Other factors that can influence the width include the mass distribution and rotation of the ellipsoid.

4. Why is the widest point on an ellipsoid important?

The widest point on an ellipsoid is important because it can provide information about the shape and size of the ellipsoid. It is also used in various mathematical and scientific calculations, such as determining the Earth's equatorial diameter.

5. How does the widest point on an ellipsoid differ from the Earth's circumference?

The widest point on an ellipsoid is different from the Earth's circumference because an ellipsoid is an irregular shape, while the Earth's circumference is a perfect circle. The widest point on an ellipsoid is also not a fixed distance, as it can vary depending on the axes and other factors.

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