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ELLIPSOID

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Originally appearing in Volume V09, Page 293 of the 1911 Encyclopedia Britannica.
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ELLIPSOID , a See also:

quadric See also:surface whose sections are ellipses. Analytically, it has for its See also:equation xz/See also:a2+y2/b2+z2/c2 =1, a, b, c being its axes; the name is also given to the solid contained by this surface (see See also:GEOMETRY: See also:Analytical). The solids and surfaces of revolution of the See also:ellipse are sometimes termed ellipsoids, but it is advisable to use the name See also:spheroid (q.v.). The ellipsoid appears in the mathematical investigation of See also:physical properties of See also:media in which the particular See also:property varies in three directions within the media; such properties are the See also:elasticity, giving rise to the See also:strain ellipsoid, thermal expansion, ellipsoid of expansion, thermal See also:conduction, refractive See also:index (see See also:CRYSTALLOGRAPHY), &c. In See also:mechanics, the ellipsoid of gyration or inertia is such that the perpendicular from the centre to a tangent See also:plane is equal to the See also:radius of gyration of the given See also:body about the perpendicular as See also:axis; the " momental ellipsoid," also termed the " inverse ellipsoid of inertia " or See also:Poinsot's ellipsoid, has the perpendicular inversely proportionalto the radius of gyration; the " equimomental ellipsoid " is such that its moments of inertia about all axes are the same as those of a given body.

End of Article: ELLIPSOID

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