Tangente (geometria)

Em verde, a reta tangente da circunferência.

Na geometria, a tangente de uma curva em um ponto P pertencente a ela, é uma reta definida a partir de um outro ponto Q pertencente à curva, muito próximo do ponto P. Ao traçarmos uma reta r que passa pelos dois pontos, é a posição para onde a reta r tende, à medida que Q se aproxima de P, "caminhando" sobre a curva. Gottfried Wilhelm Leibniz definiu-a como uma linha infinitesimal em relação ao ponto da curva que ela cruza. Em linhas gerais, uma reta se torna tangente de uma curva y = f(x) no ponto x = c, se esta passar pelo par ordenado (c, f(c)) e ter inclinação f'(c), na qual f' é derivada de f.[1] A reta tangente a um ponto de uma curva diferenciável também pode ser pensada como o gráfico da função afim que melhor aproxima a função original no ponto dado.[2]

Círculos tangentes

Dois círculos de raios não iguais, tanto no mesmo plano, são referidos como sendo tangentes entre si se eles se encontram em somente um ponto. Equivalentemente, dois círculos, com raios de ri e centros (xi, yi), para i = 1, 2 são referidos como sendo tangentes entre si se e somente se

  • Dois círculos são externamente tangentes se a distância entre seus centros for igual a soma de seus raios:
  • Dois círculos são internamente tangentes se a distância entre seus centros for igual a diferença de seus raios:[3]

Gráfico

[4]Gráfico.[5]

Referências

  1. J. Edwards (1892). Differential Calculus. London: MacMillan and Co. pp. 143 ff. 
  2. Dan Sloughter (2000) . "Best Affine Approximations"
  3. Circles For Leaving Certificate Honours Mathematics Thomas O’Sullivan. 1997
  4. «Confira este exemplo e faça outros com O Monitor». omonitor.io. Consultado em 18 de março de 2016 
  5. «Confira este exemplo e faça outros com O Monitor». omonitor.io. Consultado em 18 de março de 2016 

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