ellipsoïde

An ellipsoid is a quadric surface in three-dimensional Euclidean space. It is a generalization of a sphere and can be thought of as a stretched or compressed sphere. An ellipsoid is defined by the equation (x^2 / a^2) + (y^2 / b^2) + (z^2 / c^2) = 1, where a, b, and c are positive real numbers representing the lengths of the semi-axes along the x, y, and z directions, respectively. If a = b = c, the ellipsoid reduces to a sphere.

The shape of the ellipsoid depends on the values of a, b, and c. If two of the semi-axes are equal, the ellipsoid is called a spheroid. If a = b < c, it is a prolate spheroid, resembling a rugby ball or American football. If a = b > c, it is an oblate spheroid, resembling a squashed sphere or a lentil.

Ellipsoids have various applications in physics, astronomy, and engineering. For instance, the orbits of planets around the sun are elliptical, and in three dimensions, these orbits can be approximated as ellipsoidal. In computer graphics, ellipsoids are common shapes used for modeling objects. They also appear in the study of fluid dynamics and in the description of magnetic fields. The volume of an ellipsoid is given by the formula V = (4/3) * pi * a * b * c.

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