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Let f(z, y) be analytically irreducible at 0 and f(O) = 0. Then the plane curve singularity defined by f has the same topological type as the curve defined by fk+I for some k > 0 where fi = za + yb, f2 = ffn21 + ymllZml2, = f2n31 + fin22ym2lzm22 , are defined by induction on k with distinct numerical conditions topologically invariant. Moreover, we give an easy alternate proof of Zariski's topological classification theorem of irreducible plane curve singularities.

Topological classification of irreducible plane curve singularities in terms of Weierstrass polynomials