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\title{Pick's Theorem}
\author{Sage Binder and Katherine Kosaian}
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\begin{abstract}
    We formalize Pick's theorem for finding the area of a simple
    polygon whose vertices are integral lattice points \cite{grunbaum1993pick}.
    We are inspired by John Harrison's formalization of
    Pick's theorem in HOL Light \cite{DBLP:journals/mscs/Harrison11}, but tailor our proof approach
    to avoid a primary challenge point in his formalization,
    which is proving that any polygon with more than three
    vertices can be split (in its interior) by a line between
    some two vertices.
    Our formalization involves augmenting the existing geometry
    libraries in various foundational ways
    (e.g., by adding the definition of a polygon and
    formalizing some key properties thereof). 
\end{abstract}

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