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denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the
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A generalization of Plücker's conoid is given by the parametric equations
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Plücker's conoid is the surface defined by the function of two variables:
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Modern differential geometry of curves and surfaces with
Mathematica
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in space, we can write the above function into parametric equations
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436:{\displaystyle x=v\cos u,\quad y=v\sin u,\quad z=\sin nu.}
330:{\displaystyle x=v\cos u,\quad y=v\sin u,\quad z=\sin 2u.}
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658:, 3rd ed. Boca Raton, Florida:CRC Press, 2006.
91:but its sources remain unclear because it lacks
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227:{\displaystyle z={\frac {2xy}{x^{2}+y^{2}}}.}
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674:Geometry of curves and surfaces with MAPLE
351:with the oscillatory motion (with period 2
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122:Learn how and when to remove this message
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146:named after the German mathematician
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597:Animation of Plucker's conoid with
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654:A. Gray, E. Abbena, S. Salamon,
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23:Figure 1. Plücker's conoid with
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340:Thus Plücker's conoid is a
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16:Right conoid ruled surface
801:Algebraic geometry stubs
77:This article includes a
672:Vladimir Y. Rovenskii,
250:cylindrical coordinates
106:more precise citations.
735:–related article is a
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796:Eponyms in geometry
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702:"Plücker's Conoid"
699:Weisstein, Eric W.
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98:Please help
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104:introducing
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649:References
156:cylindroid
707:MathWorld
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248:By using
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627:See also
136:geometry
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241:at the
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446:where
243:origin
731:This
455:-axis
349:-axis
142:is a
85:, or
737:stub
680:ISBN
663:ISBN
620:= 4
602:= 3
584:= 2
566:= 3
548:= 2
530:= 2
511:= 3
496:= 2
482:= 3
457:is
419:sin
400:sin
378:cos
313:sin
294:sin
272:cos
154:or
134:In
58:= 4
43:= 3
28:= 2
782::
704:.
484:)
463:2π
245:.
162:.
138:,
89:,
81:,
768:e
761:t
754:v
743:.
710:.
686:)
678:(
669:)
661:(
618:n
600:n
582:n
564:n
546:n
528:n
509:n
498:.
494:n
480:n
470:n
466:/
453:z
448:n
431:.
428:u
425:n
416:=
413:z
409:,
406:u
397:v
394:=
391:y
387:,
384:u
375:v
372:=
369:x
353:π
347:z
325:.
322:u
319:2
310:=
307:z
303:,
300:u
291:v
288:=
285:y
281:,
278:u
269:v
266:=
263:x
222:.
214:2
210:y
206:+
201:2
197:x
191:y
188:x
185:2
179:=
176:z
125:)
119:(
114:)
110:(
96:.
60:.
56:n
45:.
41:n
30:.
26:n
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
