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model of the surface described, which is singly ruled, has a line of self-intersection, and if seen from some angles can be casually mistaken for a hyperboloid. I cannot find a viewpoint at which the two "limbs" of the figure are as symmetrical as in the photograph in question. Note also that in
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at U. Arizona, but that caption seems incorrect. Indeed, this model looks suspiciously similar to the "quartic surface with double line" model (number 52 in that page). Check carefully the wires and how they cross, and compare with those of a true doubly ruled hyperboloid (number 68). The quartic
719:. If I understand it at all correctly, it refers to the "equator" or "waistline" of the hyperboloid, which is not a straight line segment at all but a circle which contains the centers of the wires and is parallel to the circles containing their ends. Deleting that sentence. --
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A hyperboloid is a doubly-ruled surface generated by a set of straight wires, whose ends span two parallel circles in opposite senses. Note the isolated straight line segment that lies on the surface (at its narrowest part) and intercepts all the
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3. The section "Tangent planes, developable surfaces" should be rewritten, and "Application and history of developable surfaces" should be a subsection "Tangent planes, developable surfaces", not its own section.
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plane tilted 45 degrees relative to both axes and passing through the point (ε,0,0) where ε is a sufficiently small positive number. This line crosses the surface 4 times.
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It seems that the U Arizona page has been silently corrected. I have updated the image at commons, but it may take some time for the changes to become visible here.
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question: what is the significance of ruled surfaces in the history of geometry? What is its place in today geometry? is it just of historical/curiosity interest?
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indeed a hyperboloid of one sheet? The description of the image in
Knowledge and Wiki Commons were taken from the caption of item 51 in the
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surface, I gather, is obtained when two points of the generating line move along two parallel circles in
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Look again. It is not. For one thing, it is self-intersecting and has two pinch points. All the best, --
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488:{\displaystyle \left\{{\begin{array}{l}X(u,v)=Au\sin(v)\\Y(u,v)=\cos(v)\\Z(u,v)=u\end{array}}\right.}
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The fact that the surface is (at least) 4th degree is proved by considering a line parallel to the
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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2. The formatting. I have already made some strides on this, but there is more to be done.
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Well, I fixed the caption to say what the picture actually seems to show. All the best, --
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543:(a 3rd degree surface) except that the generating paabolas are replaced by circles.
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I'd like to see a citation of this, I did not find this proposition elsewhere.
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can't be right, as straight lines don't even make sense in this context.
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to different values. The two generating circles are obtained by setting
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from the wrong one (described by Stolfi) to a correct hyperboloid. â
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I repeat the question. Knowledge does not need that embarassment...
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is incorrect, I suggest you contact the authors of that page.
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equatorial "straight line segment" on hyperboloid is a circle
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The second sentence does not appear in the caption at
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To understand what Stolfi is saying, I made myself a
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734:That description fits the quartic surface that
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773:Problems with this article I hope to fix
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197:This article is within the scope of
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38:It is of interest to the following
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217:Knowledge:WikiProject Technology
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571:01:33, 22 February 2010 (UTC)
556:22:04, 21 February 2010 (UTC)
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242:Significance of ruled surface
211:and see a list of open tasks.
109:and see a list of open tasks.
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302:21:52, 8 February 2010 (UTC)
257:Correctness of image caption
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539:This surface is similar to
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575:Good idea, it is done. --
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274:senses. All the best, --
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246:Moved from main article:
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314:Elliptic hyperboloid
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717:Hyperboloid
704:Hyperboloid
112:Mathematics
103:mathematics
59:Mathematics
825:Categories
562:U. Arizona
529:spanning .
326:Wolfkeeper
214:Technology
205:technology
164:Technology
658:in pairs
272:opposite
740:Tamfang
706:, said
684:Tamfang
662:Tamfang
653:POV-Ray
139:on the
30:C-class
721:Thnidu
711:wires.
610:Thnidu
318:doubly
251:Foobar
36:scale.
791:union
813:talk
764:talk
744:talk
725:talk
688:talk
666:talk
643:talk
614:talk
608:. --
606:here
581:talk
552:talk
513:=-1/
509:and
505:=+1/
343:talk
298:talk
280:talk
525:=0,
436:cos
396:sin
261:Is
131:Mid
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