Ellipsoid - Wikipedia
网页An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables.
Ellipsoid - Math.net
网页An ellipsoid is a 3D geometric figure that has an elliptical shape. It can be viewed as a stretched sphere. An ellipsoid gets its name from an ellipse. Any plane that cuts through an ellipsoid forms an ellipse. Two ellipsoids are shown in the figure below.
Ellipsoid | Surfaces, Axes, Foci | Britannica
网页Ellipsoid, closed surface of which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre. If a, b, and c are the principal semiaxes, the general …
Ellipsoid -- from Wolfram MathWorld
网页2024年8月22日 · The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/ (a^2)+ (y^2)/ (b^2)+ (z^2)/ (c^2)=1, (1) where the semi-axes are of lengths a, b, and c.
Earth ellipsoid - Wikipedia
网页An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
The ellipsoid - Math Insight
网页The ellipsoid. Equation: x2 A2 + y2 B2 + z2 C2 = 1 x 2 A 2 + y 2 B 2 + z 2 C 2 = 1. Just as an ellipse is a generalization of a circle, an ellipsoid is a generalization of a sphere. In fact, our planet Earth is not a true sphere; it's an ellipsoid, because it's a little wider than it is tall.
Ellipsoid: Definitions and Examples - Club Z! Tutoring
网页An ellipsoid is a three-dimensional shape that is symmetrical along three axes. It can be defined as the surface that results from the rotation of an ellipse about one of its axes. An ellipsoid has three semi-axes, a, b, and c, which are the lengths of the radii along the three principal axes of the ellipsoid.
Ellipsoid - Encyclopedia of Mathematics
网页2012年4月24日 · An ellipsoid is a closed central surface of the second order (see Figure 1). The canonical equation of an ellipsoid has the form $$ \frac {x^2} {a^2} + \frac {y^2} {b^2} + \frac {z^2} {c^2} = 1 $$ The positive numbers $a$, $b$ and $c$ and the segments of corresponding lengths are called the semi-axes of the ellipsoid.
4.3: The Ellipsoid - Physics LibreTexts
网页This fact is of some importance in the description of the propagation of light in a bi-axial crystal, in which one of the wavefronts is a tri-axial ellipsoid. Let us refer the ellipsoid 4.3.4 to a set of axes Ox′y′z′ such that the angles z′Oz and x′Ox are each θ, and the y′ - and y …
1.7: Quadric Surfaces - Mathematics LibreTexts
网页2020年1月17日 · Recognize the main features of ellipsoids, paraboloids, and hyperboloids. Use traces to draw the intersections of quadric surfaces with the coordinate planes.