Multicolumn proofs, align within tabular?

Question

I want to condense my assignment by laying out each solution as a table with a picture on one side and the proof on the other. To make matters worse, I need to be able to include some equation alignment within these cells (through googling, I'm finding that it may not be possible, but I'd like to find a workaround).

Essentially, I want it to lay out as follows:

enumerate
item 1 - problem
picture | proof
item 2 - problem
picture | proof

Here's my code:

\documentclass[10pt]{article}
\parindent=0pt 
\parskip=8pt
\textwidth=5in
\hoffset=.3in
\usepackage{amssymb,amsmath,amsthm,mathrsfs,color}
\usepackage[margin=1in]{geometry}
\usepackage{enumitem}
\setlist{topsep=0pt,parsep=0pt,partopsep=-0pt,itemindent=20pt}
\usepackage{tikz}
\usetikzlibrary{calc}

\pagestyle{headings}
\title{Title}
\author{Author}
\date{Date}
\begin{document}
\maketitle

\section*{\S Number}

\begin{enumerate}
  \item
    {\bf Prove/disprove the following statement: Polygons are cool.}
    \begin{tabular}{p{2in}p{3in}}
      \begin{tikzpicture} 
      \end{tikzpicture}
    & 
      {\it Proof.} The proof is trivial! Just view the problem as a dihedral algebra whose elements are Cauchy manifolds. Then
      \begin{align*}
        x &= y \\
        &= (y^{1/2})^2 \\
        &= (z)^2.
      \end{align*}
      Voi-la! \qed
    \end{tabular}
\end{enumerate}

\end{document}

Answer 1

I would be tempted to use minipages for this- you'll have to wrap the align in some kind of vertical box regardless of the approach

\documentclass[10pt]{article}
\usepackage{amsmath,amsthm}
\usepackage{tikz}

\begin{document}

\begin{enumerate}
    \item {\bfseries Prove/disprove the following statement: Polygons are cool.} 

    \begin{minipage}{.5\textwidth}
        \begin{tikzpicture} 
            \draw circle (2cm);
        \end{tikzpicture}
    \end{minipage}%
    \begin{minipage}{.5\textwidth}
        {\itshape Proof.} 
        The proof is trivial! Just view the problem as a dihedral algebra whose elements are Cauchy manifolds. Then
        \begin{align*}
            x & = y           \\
              & = (y^{1/2})^2 \\
              & = (z)^2.      
        \end{align*}
        Voi-la! \qed
    \end{minipage}
\end{enumerate}

\end{document}

You could also have a look at the parcolumns package.

Note that in the above I have used \bfseries instead of \bf and \itshape instead of \it as discussed in (for example) "Correct" way to bold/italicize text?

Answer 2

Here's one solution. Put things in boxes before the enumeration

\documentclass[10pt]{article}
\parindent=0pt 
\parskip=8pt
\textwidth=5in
\hoffset=.3in
\usepackage{amssymb,amsmath,amsthm,mathrsfs,color}
\usepackage[margin=1in]{geometry}
\usepackage{enumitem}
\setlist{topsep=0pt,parsep=0pt,partopsep=-0pt,itemindent=20pt}
\usepackage{tikz}
%\usetikzlibrary{calc}

\pagestyle{headings}
\title{Title}
\author{Author}
\date{Date}
\begin{document}
\maketitle

\section*{\S Number}

\newsavebox{\prffg}
\savebox{\prffg}{%
%      \begin{tikzpicture} 
       \fbox{This is a Figure box\rule[-5ex]{0ex}{10ex}}
%      \end{tikzpicture}
}
\newsavebox{\prfeq}
\savebox{\prfeq}{%
      $\begin{array}{ll}
        x &= y \\
        &= (y^{1/2})^2 \\
        &= (z)^2.
      \end{array}$
}

\begin{enumerate}
  \item
    {\bf Prove/disprove the following statement: Polygons are cool.}

    \begin{tabular}{p{2in}|p{3in}}
      \usebox{\prffg}
    & 
      \begin{tabular}{p{3in}}
        {\it Proof.} The proof is trivial! Just view the problem as a
         dihedral algebra whose elements are Cauchy manifolds. Then\\
        \usebox{\prfeq}\\
        Voi-la! \qed\\
      \end{tabular}
    \end{tabular}
\end{enumerate}
\end{document}