  The Basel problem, solved by Leonhard Euler in 1734, asks to resolve
$\zeta(2)$, the sum of the reciprocals of the squares of the natural numbers,
i.e. the sum of the infinite series: \begin{equation}
\sum_{i=1}^{\infty}\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots\notag
\end{equation} The same question is posed regarding the summation of the
reciprocals of the cubes of the natural numbers, $\zeta(3)$. The resulting
constant is known as Apery's constant. A YouTube channel, 3BlueBrown, produced
a video entitled, "Why is pi here? And why is it squared? A geometric answer to
the Basel problem". The video presents the work of John W\"astlund. The
equations can be extended to $\zeta(n)$, but the geometric argument is lost. We
try to explore these equations for $\zeta(n)$.
