Em termos simples, em matemática, uma curva plana é aquela curva que se situa em um só plano euclidiano e que pode ser aberta (reta, parábola, hipérbole) ou fechada, (círculo, elipse), entre outras.Os casos mais frequentemente estudados são curvas suaves, diferenciáveis (incluindo curvas suaves de funções definidas em trechos) e curvas planas algébricas.

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  • In mathematics, a plane curve is a curve in a Euclidean plane (compare with space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.A smooth plane curve is a curve in a real Euclidean plane R2 and is a one-dimensional smooth manifold. Equivalently, a smooth plane curve can be given locally by an equation ƒ(x,y) = 0, where ƒ : R2 → R is a smooth function, and the partial derivatives ∂ƒ/∂x and ∂ƒ/∂y are never both 0. In other words, a smooth plane curve is a plane curve which "locally looks like a line" with respect to a smooth change of coordinates.An algebraic plane curve is a curve in an affine or projective plane given by one polynomial equation ƒ(x,y) = 0 (or ƒ(x,y,z) = 0, where ƒ is a homogeneous polynomial, in the projective case.)Algebraic curves were studied extensively in the 18th to 20th centuries, leading to a very rich and deep theory. Some founders of the theory are considered to be Isaac Newton and Bernhard Riemann, with main contributors being Niels Henrik Abel, Henri Poincaré, Max Noether, among others. Every algebraic plane curve has a degree, the degree of the defining equation, which is equal, in case of an algebraically closed field, to the number of intersections of the curve with a line in general position. For example, the circle given by the equation x2 + y2 = 1 has degree 2.An important classical result states that every non-singular plane curve of degree 2 in a projective plane is isomorphic to the projection of the circle x2 + y2 = 1. However, the theory of plane curves of degree 3 is already very deep, and connected with the Weierstrass's theory of bi-periodic complex analytic functions (cf. elliptic curves, Weierstrass P-function).
  • Fájl:Sikgorbe-1.jpgA síkgörbék egydimenziós síkbeli ponthalmazok Sablon:Forrás?. Vannak összefüggőek és több ágra osztottak, korlátosak és végtelenbe nyúlók. Némelyek alig, mások jobban eltérnek az egyenestől. Az egyszerű görbéken nincsenek hurkok, más görbék önmagukat metszik. A síkgörbéket többféle gyakorlati és elméleti vizsgálatnál használjuk. Megadásuk, definíciójuk nagyon változatos. Sok nevezetes görbe többféleképpen értelmezhező, ennek következtében a görbék osztályozására nem kerülhet sor, csupán jellemző típusokat tudunk kiemelni.(A matematikai elemzés során az egyenest is közéjük soroljuk.)
  • Em termos simples, em matemática, uma curva plana é aquela curva que se situa em um só plano euclidiano e que pode ser aberta (reta, parábola, hipérbole) ou fechada, (círculo, elipse), entre outras.Os casos mais frequentemente estudados são curvas suaves, diferenciáveis (incluindo curvas suaves de funções definidas em trechos) e curvas planas algébricas.
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  • Em termos simples, em matemática, uma curva plana é aquela curva que se situa em um só plano euclidiano e que pode ser aberta (reta, parábola, hipérbole) ou fechada, (círculo, elipse), entre outras.Os casos mais frequentemente estudados são curvas suaves, diferenciáveis (incluindo curvas suaves de funções definidas em trechos) e curvas planas algébricas.
  • In mathematics, a plane curve is a curve in a Euclidean plane (compare with space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.A smooth plane curve is a curve in a real Euclidean plane R2 and is a one-dimensional smooth manifold.
  • Fájl:Sikgorbe-1.jpgA síkgörbék egydimenziós síkbeli ponthalmazok Sablon:Forrás?. Vannak összefüggőek és több ágra osztottak, korlátosak és végtelenbe nyúlók. Némelyek alig, mások jobban eltérnek az egyenestől. Az egyszerű görbéken nincsenek hurkok, más görbék önmagukat metszik. A síkgörbéket többféle gyakorlati és elméleti vizsgálatnál használjuk. Megadásuk, definíciójuk nagyon változatos.
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  • Courbe plane
  • Curva piana
  • Curva plana
  • Plane curve
  • Síkgörbe
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