Cómo doblar texto para que siga las curvas de un diagrama de Venn

Question

Necesito hacer que "clase A", "clase B", "clase C" sigan las curvas de los círculos que las contienen inmediatamente:

\documentclass{article}

\usepackage[english]{babel}

\usepackage[utf8]{inputenc}

\usepackage{amsmath}

\usepackage{tikz}

\usetikzlibrary{arrows.meta}
\usetikzlibrary{decorations.text}

\begin{document}

\begin{tikzpicture}[scale=0.85]
\foreach \X [count=\Y starting from 2] in {\textit{A},\textit{B},\textit{C}}
{\draw (-\Y,-\Y/2) circle ({1.5*\Y} and \Y);
\node at (1-2*\Y,-1.1*\Y) {$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $  $ $   classes \X}; }
\draw ([xshift=-0.5cm,yshift=-0.5cm]current bounding box.south west)
rectangle ([xshift=0.5cm,yshift=0.5cm]current bounding box.north east);
\node[anchor=south] at (current bounding box.north) {\textbf{Three classes}};
\end{tikzpicture}


\end{document}

Answer 1

¿Algo como esto?

\documentclass{article}

\usepackage[english]{babel}

\usepackage[utf8]{inputenc}

\usepackage{amsmath}

\usepackage{tikz}

\usetikzlibrary{arrows.meta} 
\usetikzlibrary{decorations.text}

\begin{document}

\begin{tikzpicture}[scale=0.85] 
\foreach \X [count=\Y starting from 2] in 
{A,B,C} 
{\draw (-\Y,-\Y/2) circle ({1.5*\Y} and \Y);
\path[decoration={text along path,
text={classes |\itshape|\X},text align=center,raise=0.2em},decorate] (-\Y,-\Y/2) +(-1.5*\Y,0) arc(180:360:{1.5*\Y} and \Y);
} 
\draw ([xshift=-0.5cm,yshift=-0.5cm]current bounding box.south west) 
rectangle ([xshift=0.5cm,yshift=0.5cm]current bounding box.north east); 
\node[anchor=south] at (current bounding box.north) {\textbf{Three classes}}; 
\end{tikzpicture}

\end{document}`