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Ruled surface


Ruled surface: In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone. Other examples are a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space.

Printed dictionaries and other books with definitions for Ruled surface

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Google previewMap Projections (2006)

Cartographic Information Systems by Erik W. Grafarend, Friedrich W. Krumm

A surface is called ruled surface if there exists a parameterization of the continuity class C2 of type X(U,V) = x(U) + VY (U), where x(U) is a differentiable curve and Y (U) is a vector field along the curve x(U) which vanishes nowhere.

Google previewKinematic Differential Geometry and Saddle Synthesis of Linkages (2015)

by Delun Wang, Wei Wang

The hyperboloid XRC The constant parameter ruled surface is a hyperboloid XRC if the striction curve is a circle, which corresponds to a binary link R–C. From equation (3.131), the three construction parameters satisfy y + aff = 0, a - 6 y # 0 ...

Google previewAdvances in Algebraic Geometry Codes (2008)

by Edgar Martinez-Moro

Ruled surfaces and generalizations A ruled surface is a surface X with a mapping π : X → C to a smooth curve C, whose fibers over all points of C are P1's. Moreover, it is usually required that π has a section, that is, a mapping σ : C → X such ...

Google previewHandbook of Research on Visual Computing and Emerging Geometrical Design Tools (2016)

by Amoruso, Giuseppe

Ruled Surface: A ruled surface is a surface that can be generated by moving a line in space. The Gaussian curvature on a ruled regular surface is everywhere non-positive. Virtual Laboratory: A virtual laboratory ...

Google previewMathematical Handbook for Scientists and Engineers (2013)

Definitions, Theorems, and Formulas for Reference and Review by Granino A. Korn, Theresa M. Korn

A ruled surface is a surface generated by the displacement of a straight line (generator, generatrix). A cylinder is a surface generated by the displacement of a ...

Google previewDictionary of Classical and Theoretical Mathematics (2001)

by Catherine Cavagnaro, William T. Haight, II

developable surface A ruled surface is a surface swept out by a straight line ( called the generator) moving through space. It can be given a parameterization of the ...

Google previewA Visual Dictionary of Architecture (2011)

by Francis D. K. Ching

ruled surface A surface generated by the motion ofa straight line. Because of its straight-line geometry, a ruled surface is generally easierto form and construct than a rotational ortranslational surface. conoid A ruled surface generated by ...

Google previewEncyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

ruled surfaces (cf. Ruled surface); b) two- dimensional ...

Google previewEncyclopaedia of Mathematics (2013)

Coproduct — Hausdorff — Young Inequalities by M. Hazewinkel

AMS 1980 Subject Classification: 14M12 DEVELOPABLE SURFACE, torse - A ruled surface of zero Gaussian curvature. At all the points on one generator a developable surface has the same tangent plane. The distribution parameter of a ...

Google previewDictionary of Architectural and Building Technology (2004)

by Henry J. Cowan, Peter R. Smith, W. K. Chow

ruled surface A surface on which it is possible to draw straight lines. Consequently such a surface can be generated by a straight line, and concrete formwork can be constructed from straight ...

Google previewA dictionary of science, literature and art, ed. by W.T. Brande assisted by J. Cauvin. ed. by W.T. Brande and G.W. Cox.3 vols (1866)

by William Thomas Brande

A ruled surface of the second order, whose plane sections are either hyperbolas or parabolas. For the method of generating such a surface, see Qoadhic. The equation of the surface may be reduced to the form z *=X-— ...

Google previewThe Encyclopaedia Britannica (1902)

latest edition. A dictionary of arts, sciences and general literature by Day Otis Kellogg, William Robertson Smith

In this case, corresponding points will be joined by lines which do not lie in a plane, out on some surface, which lace ovary surface generated by lines is called a ruled surface. This surface clearly contains the bases of the two rows. If the points ...

Google previewThe New International Encyclopaedia (1904)

by Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby

A surface through every point of which a straight line may be drawn so as to lie entirely in the surface is called a ruled surface. Any one of these lines which lies on the surface is ...

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Ruled Surface at Night

Roof of Spohrer Center, art by Siefert Surface

Photo credit: NMC Second Life

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