Singular Point of a Curve
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High Quality Content by WIKIPEDIA articles! A singular point on a curve is one where it is not smooth, for example, at a cusp. The precise definition of a singular point depends on the type of curve being studied. Algebraic curves in R2 are defined as the zero set f 1(0) for a polynomial function f:R2 R. The singular points are those points on the curve where both partial derivatives vanish, f(x,y)={partial foverpartial x}={partial foverpartial y}=0. A parameterized curve in R2 is defined as the image of a function g:R R2, g(t) = (g1(t),g2(t)). The singular points are those points where {dg_1over dt}={dg_2over dt}=0.…mehr

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High Quality Content by WIKIPEDIA articles! A singular point on a curve is one where it is not smooth, for example, at a cusp. The precise definition of a singular point depends on the type of curve being studied. Algebraic curves in R2 are defined as the zero set f 1(0) for a polynomial function f:R2 R. The singular points are those points on the curve where both partial derivatives vanish, f(x,y)={partial foverpartial x}={partial foverpartial y}=0. A parameterized curve in R2 is defined as the image of a function g:R R2, g(t) = (g1(t),g2(t)). The singular points are those points where {dg_1over dt}={dg_2over dt}=0.