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# Ruled surface

## Explanation

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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### Map 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.

### Kinematic 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 ...

### Advances 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 ...

### Handbook 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 ...

### Mathematical 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 ...

### Dictionary 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 ...

### A 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 ...

### Encyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

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

### Encyclopaedia 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 ...

### Dictionary 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 ...

### A 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-— ...

### The 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 ...

### The 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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## Photo about Ruled surface

Ruled Surface at Night

Roof of Spohrer Center, art by Siefert Surface

Photo credit: NMC Second Life