Mexican hat in TikZ

Question

How would we typeset a “mexican hat” like the following

in TikZ?

Answer 1

Well the top of the hat looks like a statistical normal distribution. So I would plot that function. Furthermore you could use an arc for the upper part of the hat. And at last you could use a curve for the lower part of the hat. I have tried producing the hat with the following code:

\begin{tikzpicture}[scale=3]
\draw[very thick,domain=-1.5:1.5,xscale=0.5,smooth,variable=\x] plot ({\x},{(1.3*2.718281828^(-0.5*\x*\x))});
\draw[very thick] (0,-0 cm) arc (-90:70:1.5 cm and 0.4 cm);
\draw[very thick] (0,-0 cm) arc (270:110:1.5 cm and 0.4 cm);
\begin{scope}[yshift=0.4 cm]
\draw[very thick] (-10 : -1.5 cm and 0.4 cm) .. controls (-1.25,-0.8) and (1.25,-0.8) .. (-170 : -1.5 cm and 0.4 cm);
\end{scope}
\end{tikzpicture}

I agree it's not perfect, but feel free to improve. :D

Answer 2

I used arcs and a sin, cos combination to draw the hat (feel free to improve it):

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[ultra thick]
  \draw (2,-1.5) cos (3,0) sin (4,1.5) cos (5,0) sin (6,-1.5);
  \draw (2.4,-0.5) arc (114:428:4cm and 1cm);
  \draw (.55,-2.5) arc (210:330:4cm and 1cm);
  \draw (0.02,-1.45) arc (180:245:1.25cm);
  \draw (7.3,-2.57) arc (295:360:1.25cm);
\end{tikzpicture}

\end{document}