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Encyclopedia Britannica



CONOID (Gr. KWvor, cone, and el os, form)

This article appears in Volume V06, Page 964 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: COM-COR
CONOID (Gr. KWvor, cone, and el os, form) , in geometry, the solids (or surfaces) formed by the revolution of a conic
section
  about one of its
principal
  axes. If the conic be a circle the conoid is a sphere (q.v.); if an ellipse a spheroid (q.v.); if a
parabola
  a paraboloid; if a
hyperbola
  the surface is a hyperboloid of either one or two sheets according as the revolution takes
place
  about the conjugate or transverse
axis
 , and the surface generated by the asymptotes is called the " asymptotic
cone
 ." If two intersecting straight lines be regarded as a conic, then the
principal
  axes are the bisectors of the angles between the lines; consequently the corresponding conoid is a right circular
cone
 . It is to be noted that all these surfaces are surfaces of revolution; and they, therefore, differ from the surfaces discussed under the same names in the
article
  GEOMETRY: Analytical.
The spheroid has for its cartesian equation(x2+y2)/a2+z2/b2 = 1; the hyperboloid of one
sheet
 (of revolution)is(x2+y2)/a2-z2/b2=1; the hyperboloid of two sheets is z2/c2-(x2+y2)/a2=1; and the paraboloid of revolution is x2+y2=4az.


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