| 11. | Although, associated ruled surfaces were classical objects.
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| 12. | The hyperbolic paraboloid is a doubly ruled surface : it contains two families of mutually skew lines.
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| 13. | Edge made a " systematic classification of the quintic and sextic ruled surfaces of three-dimensional projective space ."
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| 14. | Edge s dissertation extended Luigi Cremona s 1868 delineation of the quadric ruled surfaces in projective 3-space "'RP "'3.
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| 15. | When the idea of introducing vineyards out where Spanish daggers and cactus rule surfaced, there were plenty of doubters.
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| 16. | A Clifford surface is thus a ruled surface since every point is on two lines, each contained in the surface.
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| 17. | Out of this work came another of Wren's important mathematical results, namely that the hyperboloid of revolution is a ruled surface.
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| 18. | In his later designs, ruled surfaces are prominent in the nave's vaults and windows and the surfaces of the Passion fa�ade.
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| 19. | Rational surfaces and more generally ruled surfaces ( these include quadrics and cubic surfaces in projective 3-space ) have the simplest geometry.
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| 20. | In the exceptional cases the intersection of the quadrics through the canonical curve is respectively a ruled surface and a Veronese surface.
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