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2. Ellipse - Wikipedia

   en.wikipedia.org/wiki/Ellipse

   An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

3. Six-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Six-dimensional_space

   One example is the surface of the 6-sphere, S 6. This is the set of all points in seven-dimensional space (Euclidean) that are a fixed distance from the origin. This constraint reduces the number of coordinates needed to describe a point on the 6-sphere by one, so it has six dimensions.

4. Principal axis theorem - Wikipedia

   en.wikipedia.org/wiki/Principal_axis_theorem

   The equation is for an ellipse, since both eigenvalues are positive. (Otherwise, if one were positive and the other negative, it would be a hyperbola.) The principal axes are the lines spanned by the eigenvectors. The minimum and maximum distances to the origin can be read off the equation in diagonal form.

5. Earth ellipsoid - Wikipedia

   en.wikipedia.org/wiki/Earth_ellipsoid

   The shape of an ellipsoid of revolution is determined by the shape parameters of that ellipse. The semi-major axis of the ellipse, a, becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid.

6. Ellipsoid - Wikipedia

   en.wikipedia.org/wiki/Ellipsoid

   Any ellipsoid is the image of the unit sphere under some affine transformation, and any plane is the image of some other plane under the same transformation. So, because affine transformations map circles to ellipses, the intersection of a plane with an ellipsoid is an ellipse or a single point, or is empty. [8] Obviously, spheroids contain ...

7. Eccentricity (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Eccentricity_(mathematics)

   For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...