The Ruled Surface Nature of Hyperbolic Paraboloid and Its Applications

Guoxiang GUI

Abstract


In geometry, the curved surface formed by the movement of a straight line is called a ruled surface, and the hyperbolic paraboloid is a typical ruled surface. In this study, by analyzing the image and properties of the hyperbolic paraboloid, the related geometric properties are listed. Its ruled surface nature was proved by constructing a straight generatrix on the curved surface, and the related theorem of straight generatrix was obtained. Due to the advantages of ruled surface nature, the hyperbolic paraboloid has a wide range of applications in daily life, including construction, machinery, and water conservancy, etc.


Keywords


Hyperbolic paraboloid; Ruled surface; Application

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References


Lü, L., & Xu, Z. Z. (2001). Analytic geometry. Beijing: Higher Education Press.

Wang, J. G., & Fu, R. R. (1999). Spatial analytic geometry. Beijing: Beijing Normal University Press.

Zhang, Z. J., et al. (1995). Application and teaching of ruled surface. Journal of Hebei University of Coal and Architecture, (4), 1-2.




DOI: http://dx.doi.org/10.3968/11965

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