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Added section on math brackets

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Kenneth John Odle 2023-07-22 11:28:38 -04:00
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7
bib/sites.bib
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@ -1,8 +1,11 @@
@misc{website:overleaf001,
title = "Page size and margins",
author = "Overleaf",
howpublished = "\url{https://www.overleaf.com/learn/latex/Page_size_and_margins}",
year= "No date"
}
@misc{website:overleaf002,
author = "Overleaf",
howpublished = "\url{https://www.overleaf.com/learn/latex/Brackets_and_Parentheses}",
}
@misc{website:wikibooks001,

95
lbol.tex
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@ -41,7 +41,7 @@
%\renewcommand{\footrulewidth}{0.5pt}
% Make a nice border and box for the tops of our examples
\newcommand\klab[3]{\vspace{#1}\noindent{}\hrulefill\fbox{\texttt{~#2~}}\hrulefill\vspace{#3}}
\newcommand\klab[3]{\vspace{#1}\noindent{}\hrulefill~~\fbox{\texttt{~#2~}}~~\hrulefill\vspace{#3}}
% Add an \hrule with space above and below
\newcommand\krule[2]{\vspace{#1}\hrule\vspace{#2}}
@ -705,6 +705,99 @@ The Pythagorean Theorem is \[x^2 + y^2 = z^2\]
The Pythagorean Theorem is \[x^2 + y^2 = z^2\]
\section{Brackets and Parentheses}
Brackets and parentheses are common in mathematical formulas, so it is natural that \LaTeX{} has a number of ways of typesetting these.
% Provide some additional spacing in this table; may move this to preamble later
\setlength{\tabcolsep}{14pt}
\renewcommand{\arraystretch}{1.4}
\begin{table}[H]
\centering
\caption{Brackets and Parentheses\label{brackpar}}
\medskip
\noindent{}\begin{tabular}{| m{3.5cm} m{3cm} m{1.5cm} |}
\hline
\textbf{Type} & \textbf{Code} & \textbf{Example} \\
\hline
Parentheses; \newline round brackets & \verb|(a+b)| & $(a+b)$ \\
\hline
Brackets; \newline square brackets & \verb|[a+b]| & $[a+b]$ \\
\hline
Braces; curly brackets & \verb|\{a+b\}| & \{a+b\} \\
\hline
Angle brackets & \verb|\langle a+b \rangle| & $\langle a+b \rangle$ \\
\hline
Pipes & \verb:|a+b|: & $|a+b|$ \\
\hline
Double Pipes & \verb:\|a+b\|: & $\|a+b\|$ \\
\hline
\end{tabular}
\end{table}
\subsection{Adjusting Size Dynamically}
To dynamically size brackets and parentheses, you can use \verb+\left+ and \verb+\right+ commands. For example, this code
\begin{Verbatim}[frame=lines, numbers=left, xleftmargin=5mm, framesep=3mm]
\[
F=G \left( \frac{m_1 m_2}{r^2} \right)
\]
\end{Verbatim}
produces this output:
\[
F=G \left( \frac{m_1 m_2}{r^2} \right)
\]
Note that \textit{both} commands are required.
If you are writing a multi-line equations in an \texttt{align}, \texttt{align*}, or \texttt{aligned} environment, you must balance \verb+\left+ and \verb+\right+ both on each line, and on the same side of the \texttt{\&} delimiter. If an opening or closing bracket is not required, you can use an invisible bracket to balance them, i.e., \verb+\left.+ and \verb+\right.+.
\subsection{Adjusting Size Explicitly}
You can also control the size of brackets and parentheses explicitly:
% Provide some additional spacing in this table; may move this to preamble later
\setlength{\tabcolsep}{14pt}
\renewcommand{\arraystretch}{1.6}
\begin{table}[H]
\centering
\caption{Explicit Size Commands\label{brackparexp}}
\medskip
\noindent{}\begin{tabular}{| m{7cm} m{2cm} |}
\hline
\textbf{Markup} & \textbf{Renders as} \\
\hline
\verb+\bigl( \Bigl( \biggl( \Biggl(+ & $\bigl( \Bigl( \biggl( \Biggl($ \\
\hline
\verb+\bigr] \Bigr] \biggr] \Biggr]+ & $\bigr] \Bigr] \biggr] \Biggr]$ \\
\hline
\verb+\bigl\{ \Bigl\{ \biggl\{ \Biggl\{+ & $\bigl\{ \Bigl\{ \biggl\{ \Biggl\{$ \\
\hline
\verb+\bigl \langle \Bigl \langle \biggl+ \verb+\langle \Biggl \langle+ & $\bigl \langle \Bigl \langle \biggl \langle \Biggl \langle$ \\
\hline
\verb+\bigr \rangle \Bigr \rangle \biggr+ \verb+\rangle \Biggr \rangle+ & $\bigr \rangle \Bigr \rangle \biggr \rangle \Biggr \rangle$ \\
\hline
\verb+\big| \Big| \bigg| \Bigg|+ & $\big| \Big| \bigg| \Bigg|$ \\
\hline
\verb+\big\| \Big\| \bigg\| \Bigg\|+ & $\big\| \Big\| \bigg\| \Bigg\|$ \\
\hline
\verb+\bigl \lceil \Bigl \lceil \biggl+ \verb+\lceil \Biggl \lceil+ & $\bigl \lceil \Bigl \lceil \biggl \lceil \Biggl \lceil$ \\
\hline
\verb+\bigr \rceil \Bigr \rceil \biggr+ \verb+\rceil \Biggr \rceil+ & $\bigr \rceil \Bigr \rceil \biggr \rceil \Biggr \rceil$ \\
\hline
\verb+\bigl \lfloor \Bigl \lfloor \biggl+ \verb+\lfloor \Biggl \lfloor+ & $\bigl \lfloor \Bigl \lfloor \biggl \lfloor \Biggl \lfloor$ \\
\hline
\verb+\bigr \rfloor \Bigr \rfloor \biggr+ \verb+\rfloor \Biggr \rfloor+ & $\bigr \rfloor \Bigr \rfloor \biggr \rfloor \Biggr \rfloor$ \\
\hline
\end{tabular}
\end{table}
\section{The \texttt{align} Environment}
\section{The \texttt{array} Environment}