# prolate spheroid

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Related to prolate spheroid: Prolate ellipsoid

## prolate spheroid

[′prō‚lāt ′sfir‚ȯid]
(mathematics)
The ellipsoid or surface obtained by revolving an ellipse about one of its axes so that the equatorial circle has a diameter less than the length of the axis of revolution. Also known as prolate ellipsoid.
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On the other hand, the asymptotic case of the needle of length a1 can be reached by a prolate spheroid when 0 < [a.sub.3] = [a.sub.2] << [a.sub.1] < +[infinity], while, for the case where 0 < [a.sub.3] << [a.sub.2] = [a.sub.1] < +[infinity], the oblate spheroid takes the shape of a circular disk of radius [a.sub.1] = [a.sub.2].
Caption: Figure 7: Application of Mogi and prolate spheroid models to the observed mean surface deformation maps during the preeruption and coeruption periods.
It is clear that a prolate spheroid can be considered as the union of two TPSs and that is the idea we will use to present an example that shows the validity of (8), based on the result given by (3).
Here we consider the range -1/2 < [summation] < 0, corresponding to solutions for the prolate spheroid. The dimensionless rotation rates [summation] and [[OMEGA].sub.P] are related by [summation] = -[([r.sub.1]/[R.sub.0]).sup.3] [[OMEGA].sub.P].
The downside with the prolate spheroids is that percolation will occur for smaller volume fraction than spheroid particles.
We have investigated analytically the asymptotic behavior of the reflected high-order modes induced by the presence of the so-called DtN2 absorbing boundary condition when employed for solving exterior Helmholtz problems with prolate spheroid shaped scatterers.
This indicates that the nucleus is similar to a nonspherical irregular shape that can be approxi-mated by a prolate spheroid.
In light of the fact that shape and geometry potentially are independent organic variables, the species examined during this study were categorized in terms of three simple geometric classes (the sphere, the prolate spheroid, and the cylinder; although common among some organisms, such as the diatoms, the oblate spheroid was not obtained by any of the taxa examined during this study).
The prolate spheroid (8) is called the reference prolate spheroid of this coordinate system.
Our most likely prolate spheroid is depicted in Fig.
To determine cardiac volumes (end diastolic volume and end systolic volume), embryonic and larval crayfish hearts were modeled as a prolate spheroid (cardiac volume = 4/3 [pi]a[b.sup.2]), where a and b are half of the measured long and short axes of the heart, respectively (Keller et al., 1991, 1994; Taber et al., 1992; Schwerte and Pelster, 2000; and Harper and Reiber, 2001).
Gravitational effects can be peculiar, in that from an extreme example in one of my references where a "minimal" black hole of some 2.3 solar masses and about 13.7-km dia circling somewhere between the orbital latitudes of Jupiter and Saturn will exert an anomalous hug-and-squeeze effect on Earth to where it would become a prolate spheroid, having a diameter greater at the poles than the equator.

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