\documentclass[12pt]{article}
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\title{Solution to the pie problem - with the help of Justin Bieber}
\author{Alex Smout}
\begin{document}
\maketitle
\begin{abstract}
In a pledge to merge the worlds of Bieber and mathematics, all variables are chosen as the boy king's bestest songs
\end{abstract}
\section{Definition of problem}
Mathematical definition of problem. It's fairly self explanatory which variables refer to each of Volume, Crust Area, Radius, and Height
\begin{align}
\begin{split}
Beauty And A Beat &= \pi Baby^2 Boyfriend\\
\end{split}
\end{align}
\begin{align}
\begin{split}
AsLongAsYouLoveMe &= \pi Baby^2 + 2\pi Baby Boyfriend\\
\end{split}
\end{align}
\section{Solution}
Define boyfriend in terms of Baby (from (1))
\begin{align}
\begin{split}
Boyfriend &= \frac{400}{(Baby^2)}\\
\end{split}
\end{align}
Substitute (3) into (2)
\begin{align}
\begin{split}
AsLongAsyouLoveMe &= \pi Baby^2 + \frac{800\pi}{Baby}\\
\end{split}
\end{align}
Differentiate with respect to Baby and set to 0 to find minimum of AsLongAsYouLoveMe
\begin{align}
\begin{split}
2 \pi Baby - \frac{800\pi}{Baby^2} &= 0\\
2 \pi Baby^3 - 800\pi &= 0\\
Baby^3 &= 400\\
Baby &= \sqrt[3]{400}\\
&= 7.368\\
\end{split}
\end{align}
From (3)
\begin{align}
\begin{split}
Boyfriend &= \frac{400}{(Baby^2)}\\
&= \frac{400}{\sqrt[3]{400}^2}\\
&= \sqrt[3]{400}\\
&= 7.368\\
\end{split}
\end{align}
Thus also proving the long assumed conjecture that Baby == Boyfriend for all real values of Boyfriend and Baby
\end{document}
