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- Newton's_theorem_about_ovals abstract "In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant.Isaac Newton stated it as lemma 28 of section VI of book 1 of Newton's Principia, and used it to show that the position of a planet moving in an orbit is not an algebraic function of time. There has been some controversy about whether or not this theorem is correct because Newton did not state exactly what he meant by an oval, and for some interpretations of the word oval the theorem is correct, while for others it is false. If "oval" means "continuous convex curve", then there are counterexamples, such as triangles or one of the lobes of Huygens lemniscate y2 = x2 − x4, while Arnold (1989) pointed that if "oval" means "infinitely differentiable convex curve" then Newton's claim is correct and his argument has the essential steps of a rigorous proof.Vassiliev (2002) generalized Newton's theorem to higher dimensions.".
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- Newton's_theorem_about_ovals wikiPageExternalLink books?isbn=0821829483.
- Newton's_theorem_about_ovals wikiPageID "29224388".
- Newton's_theorem_about_ovals wikiPageRevisionID "598471158".
- Newton's_theorem_about_ovals hasPhotoCollection Newton's_theorem_about_ovals.
- Newton's_theorem_about_ovals subject Category:Curves.
- Newton's_theorem_about_ovals subject Category:Isaac_Newton.
- Newton's_theorem_about_ovals subject Category:Theorems_in_geometry.
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- Newton's_theorem_about_ovals type Curve113867641.
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- Newton's_theorem_about_ovals type Proposition106750804.
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- Newton's_theorem_about_ovals type Statement106722453.
- Newton's_theorem_about_ovals type Theorem106752293.
- Newton's_theorem_about_ovals type TheoremsInGeometry.
- Newton's_theorem_about_ovals comment "In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant.Isaac Newton stated it as lemma 28 of section VI of book 1 of Newton's Principia, and used it to show that the position of a planet moving in an orbit is not an algebraic function of time.".
- Newton's_theorem_about_ovals label "Newton's theorem about ovals".
- Newton's_theorem_about_ovals label "Teorema de Newton sobre ovais".
- Newton's_theorem_about_ovals sameAs Teorema_de_Newton_sobre_ovais.
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- Newton's_theorem_about_ovals sameAs Q7020025.
- Newton's_theorem_about_ovals sameAs Newton's_theorem_about_ovals.
- Newton's_theorem_about_ovals wasDerivedFrom Newton's_theorem_about_ovals?oldid=598471158.
- Newton's_theorem_about_ovals depiction Lemniscate-of-Gerono.svg.
- Newton's_theorem_about_ovals isPrimaryTopicOf Newton's_theorem_about_ovals.
