The definition of a paraboloid is a solid with two or more parabolic sections parallel to a single axis, or is a solid generated by rotating a parabola around a center point (axis).
A solid made by rotating a parabola around an axis is an example of a paraboloid.
a surface or solid formed so that sections parallel to the plane of symmetry are parabolas and sections perpendicular to it are ellipses (elliptic paraboloid), hyperbolas (hyperbolic paraboloid), or circles (paraboloid of revolution)
A surface having parabolic sections parallel to a single coordinate axis and elliptic or circular sections perpendicular to that axis.
The equation for
a circular paraboloid is
x 2a 2
A surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis.
- ZUy2BB0 Bll; reducing, when the liquid extends to infinity and B 3 =0, to = xA o' _ - zUy 2B o so that in the relative motion past the body, as when fixed in the current U parallel to xO, A 4)'=ZUx(I+Bo), 4)'= zUy2(I-B o) (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting b 2 =pa, A = A'a, and proceeding to the limit where a = oo, we find for a paraboloid of revolution P B - p (7) B = 2p +A/' Bo p+A y2 i =p+A'- 2x, (8) p+?
- With A' =0 over the surface of the paraboloid; and then' = ZU[y 2 - pJ (x2 + y2) + px ]; (9) =-2U p [1/ (x2 + y2)-x]; (io) 4, = - ZUp log [J(x2+y2)+x] (II) The relative path of a liquid particle is along a stream line 1,L'= 2Uc 2, a constant, (12) = /,2 3, 2 _ (y 2 _ C 2) 2 2 2 2' - C2 2 x 2p(y2 - c2) /' J(x2 +y 2)= py ` 2p(y2_c2)) (13) a C4; while the absolute path of a particle in space will be given by dy_ r - x _ y 2 - c2 dx_ - y - 2py y 2 - c 2 = a 2 e -x 1 46.
- A rotifer may be regarded as typically a hemisphere or half an oblate spheroid or paraboloid with a mouth somewhere on the flat end ("disk" or "corona"), which bears a usually double ciliated ring, the outer zone the "cingulum," and inner the "trochus".
- Foucault invented in 1857 the polarizer which bears his name, and in the succeeding year devised a method of giving to the speculum of reflecting telescopes the form of a spheroid or a paraboloid of revolution.
- Showed that, if the large mirror were a segment of a paraboloid of revolution whose focus is F, and the small mirror an ellipsoid of revolution whose foci are F and P respectively, the resulting image will be plane and undistorted.