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content.tex
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content.tex
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\section{The Square Root of 2}
\begin{frame}
\begin{columns}
\begin{column}{0.3\textwidth}
\centering
\begin{tikzpicture}
\draw[draw=gmitblue] (0,0) --node [midway, left, black] {$1$} (0,3) -- (3,3) -- (3,0) --node [midway, below, black] {$1$} (0,0);
\draw[gmitred] (3,0) -- (0,3) node [midway, above right, black] {$\sqrt{2}$};
\end{tikzpicture}
\end{column}
{\color{gmitgrey!30}\vrule{}} \hspace{0.1\textwidth}
\begin{column}{0.5\textwidth}
$\sqrt{2} \times \sqrt{2} = 2$ \\[16mm]
$d^2 = l^2 + w^2$ \\[4mm]
$d^2 = 1^2 + 1^2$ \\[4mm]
$d = \sqrt{2}$ \\[8mm]
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\begin{columns}
\begin{column}{0.3\textwidth}
\color{gmitblue} \fontsize{30}{10}
\[\frac{a}{b}\]
\end{column}
{\color{gmitgrey!30}\vrule{}} \hspace{0.1\textwidth}
\begin{column}{0.5\textwidth}
$\sqrt{2} = \dfrac{a}{b}$ \\[8mm]
$\Rightarrow 2 = \dfrac{a^2}{b^2}$ \\[8mm]
$\Rightarrow 2b^2 = a^2$ \\[8mm]
$\Rightarrow 2 \mid a^2$ \\[8mm]
$\Rightarrow 2 \mid a$
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\begin{columns}
\begin{column}{0.3\textwidth}
\color{gmitblue} \fontsize{30}{10}
\[2 \mid a\]
\end{column}
{\color{gmitgrey!30}\vrule{}} \hspace{0.1\textwidth}
\begin{column}{0.5\textwidth}
$2 \mid a$ \\[8mm]
$\Rightarrow 4 \mid a^2$ \\[8mm]
$\Rightarrow 4 \mid 2b^2$ \\[8mm]
$\Rightarrow 2 \mid b^2$ \\[8mm]
$\Rightarrow 2 \mid b$
\end{column}
\end{columns}
\end{frame}
\begin{frame}[standout]
\begin{quote}
A number is rational if and only if its decimal expansion becomes periodic.
\end{quote}
\end{frame}