Assertion: ellipsoid's ax | /r/HasProperty | equal
Facets:
Source sentences:
text: If two axes are equal, say a = b, and different from the third, c, then the ellipsoid is an ellipsoid of revolution, or spheroid (see the figure), the figure formed by revolving an ellipse about one of its axes.
text: Lagrange in 1811 considered the possibility of a tri-axial ellipsoid being in equilibrium, but concluded that the two equatorial axes of the ellipsoid must be equal, leading back to the solution of Maclaurin spheroid.
text: If two axes are equal, say
text: If two semi-axes of an ellipsoid are equal, the ellipsoid is called an ellipsoid of revolution, and the sections of an ellipsoid of revolution by planes parallel to the plane of the equal semi-axes are circles.
text: An important special case of the index ellipsoid occurs when the ellipsoid is an ellipsoid of revolution, i.e. constructed by rotating an ellipse around either the minor or major axis, when two axes are equal and a third is different.
text: When all axes of the index ellipsoid are equal, the material is isotropic, commonly known as cubic.
text: An important special case of the index ellipsoid occurs when the ellipsoid is an ellipsoid of revolution, i.e. constructed by rotating an ellipse around either the minor or major axis, when two axes are equal and a third is different.
text: When all axes of the index ellipsoid are equal, the material is isotropic, commonly known as cubic.
text: In the even more special case of a sphere where all three axes are equal, all the points are umbilical