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| A '''toric section''' is an intersection of a [[Plane (mathematics)|plane]] with a [[torus]], just as a [[conic section]] is the intersection of a [[Plane (mathematics)|plane]] with a [[cone (geometry)|cone]].
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| ==Mathematical formulae==
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| In general, toric sections are fourth-order ([[quartic curve|quartic]]) [[plane curve]]s of the form
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| :<math>
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| \left( x^2 + y^2 \right)^2 + a x^2 + b y^2 + cx + dy + e = 0.
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| </math> | |
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| ==Spiric sections==
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| A special case of a toric section is the [[spiric section]], in which the intersecting plane is parallel to the rotational symmetry axis of the [[torus]]. They were discovered by the ancient Greek geometer [[Perseus (geometer)|Perseus]] in roughly 150 BC. Well-known examples include the [[hippopede]] and the [[Cassini oval]] and their relatives, such as the [[lemniscate of Bernoulli]].
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| == Villarceau circles ==
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| Another special case is the [[Villarceau circles]], in which the intersection is a circle despite the lack of any of the obvious sorts of symmetry that would entail a circular cross-section.
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| ==General toric sections==
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| More complicated figures such as an [[annulus (mathematics)|annulus]] can be created when the intersecting plane is [[perpendicular]] or [[:wikt:oblique|oblique]] to the rotational symmetry axis.
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| [[Category:Algebraic curves]]
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| [[Category:Toric sections]]
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| {{geometry-stub}}
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Revision as of 09:29, 26 February 2014
Friends contact her Felicidad and her husband doesn't like it at all. Meter reading is exactly where my primary earnings arrives from but quickly I'll be on my personal. Delaware is our beginning place. Playing crochet is a factor that I'm completely addicted to.
Also visit my blog: Dotnetnuke.Joinernetworks.com