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...ast4=Torquato |first4=Salvatore |title=Unusually Dense Crystal Packings of Ellipsoids |journal=Physical Review Letters |date=23 June 2004 |volume=92 |issue=25 |p ...pha:\sqrt{\alpha}:1</math> and <math>\alpha \in (1.365,1.5625)</math>. Any ellipsoids with aspect ratios larger than one can pack denser than spheres. ...

[[File:Diphenyl-ether-from-xtal-2004-CM-3D-ellipsoids.png|thumb|left|350px|A thermal ellipsoid model of one stable [[conformation ...d the positions of atoms and the anisotropies of position reflected in the ellipsoids derive from a crystal structure of the molecule.<ref>Angshuman R. Choudhury ...

...t4=Torquato | first4=Salvatore | title=Unusually Dense Crystal Packings of Ellipsoids | journal=Physical Review Letters | publisher=American Physical Society (AP ...hn W. | last2=Wertheim | first2=M.S. | title=Statistical mechanics of hard ellipsoids. I. Overlap algorithm and the contact function | journal=Journal of Computa ...

...f second-degree surfaces" (...) "In fact a simple consideration shows that ellipsoids with three unequal axes can very well be figures of equilibrium; and that o The Jacobi and Dedekind ellipsoids are both equilibrium figures for a body of rotating homogeneous self-gravit ...

[[Category:Ellipsoids]] ...

...|last2= Kiyohara |year=2004 |title= The cut loci and the conjugate loci on ellipsoids |journal= Manuscripta Mathematica |volume=114 |issue=2 |pages=247–264 |doi ...

...rformances are correlated (as indicated by the stretch and rotation of the ellipsoids). Specifications are often defined by upper or lower limits, represented as ...

...<ref>Lebovitz, N. R. (1998). The mathematical development of the classical ellipsoids. ''International journal of engineering science'', 36(12), 1407–1420.</ref> ...ebovitz in modern form in 1965.<ref>Norman R. Lebovitz (1965), The Riemann ellipsoids (lecture notes, Inst. Ap., Cointe-Sclessin, Belgium)</ref> Let <math>a_1(t) ...

...Lebovitz NR (1962). "The Potentials and the Superpotentials of Homogeneous Ellipsoids" (PDF). Ap. J. 136: 1037–1047. {{Bibcode|1962ApJ...136.1037C}}. {{doi|10.10 ...

...x} = C </math>for varying <math>C</math>. As <math>C</math> decreases, the ellipsoids become smaller and smaller, until at its minimal value, the ellipsoid shrin ...of moving around the plane, searching for that shared center of all those ellipsoids. The center can be found by computing <math>\boldsymbol{A}^{-1}</math> exp ...

[[Category:Ellipsoids]] ...

...cipal axes-aligned quadric surfaces can be defined in QGA. These include [[ellipsoids]], [[cylinders]], [[cones]], [[paraboloids]], and [[hyperboloids]] in all o ...

| title=Ellipsoids and matrix-valued valuations ...

...projective spaces one can construct ovoids by combining halves of suitable ellipsoids such that they are no quadrics. ...

...s a result, the angular velocity vector remains on the intersection of two ellipsoids. Here, the yellow ellipsoid is the angular momentum ellipsoid, and the expa ...of <math>\omega(t)</math> must stay on the intersection curve between two ellipsoids defined by <math display="block">\begin{cases} ...

...bodies such as the [[Moon]] and [[Mars]] now have quite precise reference ellipsoids. ...rly-spherical bodies, which includes all the rocky planets and many moons, ellipsoids are defined in terms of the axis of rotation and the mean surface height ex ...

...itrary ''n'', the iso-density loci are unions of [[ellipsoid]]s. All these ellipsoids or ellipses have the common center &mu; and are scaled copies (homothets) o [[Category:Ellipsoids]] ...

...lity states that the shapes with maximum Mahler volume are the spheres and ellipsoids. The three-dimensional case of this result was [[mathematical proof|proven] ...

Superellipsoids have an rich shape vocabulary, including cuboids, cylinders, ellipsoids, octahedra and their intermediates.<ref name=":2">{{Cite book |last1=Liu |f ...graphics/superquadric-ellipsoids-and-toroids-opengl-lig-r1172 SuperQuadric Ellipsoids and Toroids, OpenGL Lighting, and Timing] ...

..._n</math> is ''n''-dimensional volume, and there is equality precisely for ellipsoids. {{harvs|txt|last=Zhang|author-link=Gaoyong Zhang|year=1991}} proved that f ...