# Split equation problem in cheatsheet?

I was trying to prepare a cheat sheet using the template posted by xport (Preparing cheat sheets)

However when I try to use "\begin{split}" I get an error

\begin{split} on input line...ended by \end{minipage}

However, if I use eqnarray it works fine. I wonder why "split" option does not work.

Below is my code,

\documentclass[table,cmyk]{article}
\usepackage[a4paper,margin=1cm,landscape]{geometry}
\usepackage{longtable,array,calc}
\usepackage{xcolor}
\usepackage{amsmath}
\makeatletter
\newcommand\ratio[2]{\strip@pt\dimexpr#1pt/#2\relax}
\newcolumntype{A}[2]
{
>{\begin{minipage}[t]{#2\linewidth-2\tabcolsep-#1\arrayrulewidth}%
\vspace{\tabcolsep}}%
c%
<{\vspace{\tabcolsep}\end{minipage}}%
}
\makeatother

\pagestyle{empty}

\arrayrulewidth=1pt
\tabcolsep=10pt
\arrayrulecolor{red}

\usepackage{lipsum}
\begin{document}
\begin{longtable}
{
|A{1.5}{\ratio{30}{100}}% 30%
|A{1}{\ratio{30}{100}}% 30%
|A{1.5}{\ratio{40}{100}}% 40%
|%
}\hline
%Cell 1,1

$$\label{eq1} \begin{split} A & = \frac{\pi r^2}{2} \\ & = \frac{1}{2} \pi r^2 \end{split}$$

The fundamental theorem of calculus,
$\int_a^b f(x)\,\textrm{d}x=F(b)-F(a)$
where $\frac{\textrm{d}F(x)}{\textrm{d}x}=f(x)$
&
%Cell 1,2
\LaTeX\ will make you confident!
&
%Cell 1,3
\lipsum[1]
\tabularnewline\hline
%Cell 2,1
The fundamental theorem of calculus,
$\int_a^b f(x)\,\textrm{d}x=F(b)-F(a)$
where $\frac{\textrm{d}F(x)}{\textrm{d}x}=f(x)$
&
%Cell 2,2
\LaTeX\ will make you confident!
&
%Cell 2,3
\lipsum[2]
\tabularnewline\hline
\end{longtable}
\end{document}


If you lose the & symbols, it works. If you replace equation with gather you get a new error message (illegal \par detected). I suspect that longtable is parsing the contents of environments, but not macros or {...} blocks.
{$$\label{eq1} \begin{split} A &= \frac{\pi r^2}{2} \\ &= \frac{1}{2} \pi r^2 \end{split}$$}