# Ellipsoid

• Oct 26th 2008, 03:34 PM
loollool
Ellipsoid
Thanks
• Oct 26th 2008, 04:47 PM
Here to Help
"The" bisector
It is incorrect to talk about "The" bisector of an ellipsoid, unlike a sphere it doesn't have just one that is the same throughout. The bisectors would be ellipses, but I am not aware of any special names given to one of them.
• Oct 26th 2008, 06:28 PM
loollool
• Oct 27th 2008, 12:32 AM
earboth
Quote:

Originally Posted by loollool
Do you mean that to bisect an ellipsoid, we need to use an ellipse?
Here is my question in other words: Is a bisector of an ellipsoid a reasonabley described curve? For instance, in the plane, it is a straight line halfway between the two points. How about in an ellipsoid?

1. In general a bisector is one dimension lower than the bisected object. For example:

the bisector of a circle (dim = 2) is a straight line (dim = 1)
the bisector of a solid (dim = 3) is a plane (dim = 2)

2. There are 2 different types of ellipsoids:
a) Elliptic ellipsoid: Then every bisector is an ellipse
b) Rotational ellipsoid: Then the bisector is either a circle (the axis of rotation is perpendicular to this circle) or an ellipse.

EDIT: After playing around a little bit I noticed that it must be possible to get a circular bisector with elliptic ellipsoids too!
• Oct 27th 2008, 09:27 AM
loollool
Thanks! It makes sense.