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281:{\displaystyle \left\{(x,y)\in \mathbf {R} ^{2}:\sum _{i=1}^{n}{\sqrt {(x-u_{i})^{2}+(y-v_{i})^{2}}}=d\right\}.}
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643:, I.M.A. Volumes in Mathematics and its Applications, 146, Springer, New York, 2008, pp. 117-132
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Examples of 3-ellipses for three given foci. The progression of the distances is not linear.
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P.V. Sahadevan (1987): "The theory of egglipse—a new curve with three focal points",
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Z.A. Melzak and J.S. Forsyth (1977): "Polyconics 1. polyellipses and optimization",
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J. Nie, P. Parrilo, B.St.: "Semidefinite representation of the k-ellipse", in
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527:"On the Approximation of Convex, Closed Plane Curves by Multifocal Ellipses"
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International
Journal of Mathematical Education in Science and Technology
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329:-ellipse is in general a subset of the points satisfying a particular
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The
Scientific Letters and Papers of James Clerk Maxwell: 1846-1862
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Generalization of the ellipse to allow more than two foci
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295:, and the 2-ellipse is the classic ellipse. Both are
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of points of the plane whose sum of distances to the
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486:-Ellipses and the Minimum Distance Sum Problem",
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54:-ellipses go by numerous other names, including
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684:The Geometry of Semidefinite Programming
434:{\displaystyle 2^{n}-{\binom {n}{n/2}}.}
658:Paper on the Description of Oval Curves
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341:, the algebraic degree of the curve is
637:J. Nie, P.A. Parrilo, B. Sturmfels: "
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81:). They were first investigated by
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79:Ehrenfried Walther von Tschirnhaus
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322:unless it goes through a focus.
641:Algorithms in Algebraic Geometry
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446:-ellipses are special cases of
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534:Journal of Applied Probability
490:106 #3 (March 1999), 193–202.
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488:American Mathematical Monthly
677:On the Construction of Ovals
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75:Tschirnhaus'sche Eikurve
46:allowing more than two
593:, pages 239–255, 1977.
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361:{\displaystyle 2^{n}}
291:The 1-ellipse is the
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571:on 28 September 2016
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654:James Clerk Maxwell
482:J. Sekino (1999): "
126:foci is a constant
83:James Clerk Maxwell
606:18 (1987), 29–39.
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331:algebraic equation
299:of degree 2.
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56:multifocal ellipse
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686:", pp. 9–16.
660:, Feb 1846, from
591:Q. of Appl. Math.
460:Generalized conic
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705:Algebraic curves
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573:. Retrieved
566:the original
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448:spectrahedra
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316:convex curve
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32:
26:
575:22 February
519:Erdős, Paul
368:, while if
60:polyellipse
694:Categories
471:References
656:(1846): "
619:613.51030
540:: 89–96.
503:986.51040
394:−
240:−
208:−
180:∑
161:∈
85:in 1846.
562:17166889
525:(1982).
454:See also
103:,
71:-ellipse
64:egglipse
36:-ellipse
29:geometry
554:3213552
495:1682340
77:(after
44:ellipse
42:of the
617:
611:872599
560:
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320:smooth
312:closed
293:circle
88:Given
73:, and
31:, the
569:(PDF)
558:S2CID
550:JSTOR
530:(PDF)
333:. If
120:locus
38:is a
577:2015
374:even
325:The
48:foci
615:Zbl
542:doi
499:Zbl
372:is
339:odd
337:is
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