THE HYPERBOLOID OF REVOLUTION OF ONE NAPPE A RULED SURFACE GENERATING CONICS
Keywords:
surface of revolutionAbstract
The paper intends to underline the property of the hyperboloid of revolution of one nappe to generate on its surface, when it is cut by a plane, the three known conics (ellipse, hyperbola and parabola).Cutting this surface by a plane, we find the equation of the section to be the general equation of a conic. Depending on the parameters of this equation, we can establish the nature of the conic. The paper intends to emphasize the property of similarity between the ruled hyperboloidal surfaces of revolution and the conic ones, regarding their capacity to “house” conics on their surfaces; it also points out the existence of an alternative for the Dandelin's theorem in the case of the hyperboloid.
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References
A., Javary, (1889). Traite de geometrie descriptive,
deuxieme partie, Librairie Ch. Delagrave, Paris
M., St. Botez, (1965). Geometrie descriptiva,
Editura Didactica si Pedagogica, Bucuresti.
A., Tanasescu, (1975). Geometrie descriptiva,
perspectiva, axonometrie, Editura Didactica si
Pedagogica, Bucuresti.
G., Oprea, (2003). Geometrie descriptiva; curs si
aplicatii, Editura Printech, Bucuresti.
D., Marin, G., Oprea, s.a, (1998). Geometrie
descriptiva. Probleme si aplicatii, Editura BREN,
Bucuresti.
G., Oprea, A., Rugescu, N., Valter, (2013). The
Graphic Determination of the Specific Elements of
the Conic Sections. Buletinul Stiintific al
Universitatii POLITEHNICA Timisoara. Tom 58
(72), pag. 9-12, ISSN 1224 – 6042
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