箭头位于螺旋曲线末端

箭头位于螺旋曲线末端

各位朋友,

这是我的 MWE。我需要绘制一个旋转不止一圈的三角螺旋线。如何在螺旋线与末端相交处放置箭头?

\begin{tikzpicture}[scale=1.5, cap=round, color = blue];
\draw [->] [thick, domain= 0  : 25.   90, variable=\t,smooth,samples=500] plot  ({\t r}:  {0.001 *\t*\t}  );
\centring
\draw[blue,very thick] (0,0)--(45:1cm) node[right]{};
\draw[blue] (1,1) node{};
\draw (45: 2cm) node{$\bullet$};
\draw [blue, thick](0,0) --(1.4142,0)node[below]{};
\draw[blue, thick](1.4142,0)--(1.4142,1.4142);
\draw( 30: 7 mm) node [  right] {$A$}; 
%nodes
\node at (0.7071, 0.7071)[ above left] {$\sqrt2$};
\node at (0.7071, 0)[ below ] {$1$};
\node at (1.4142, 0.7071)   [  right ] {$1$};
% axis 
\draw[->]  [blue, thick](0,0)--(2,0) node [right] {$x$};
\draw[->]  [blue, thick](0,0) --(0,2) node [right] {$y$};
\draw[-]  [blue, ultra thick]( 0,0) --( 1.4142,0){};
\draw[-]  [blue, ultra thick]( 0,0) --( 1.4142,1.4142 ){};
\draw( 0,0) node [below left] {};
\end{tikzpicture}

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