  In this paper we construct a visualization of the Abel's Impossibility
Theorem also known as the Abel-Ruffini Theorem. Using the canvas object in
JavaScript along with the p5.js library, and given any expression that uses
analytic functions and radicals one can always construct closed paths such that
the expression evaluated at the coefficients of a general polynomial returns to
it's initial position, while the roots of the polynomial undergo a non-trivial
permutation. Hence, such expression does not reconstruct the roots from the
coefficients. Using the visualization we begin by considering the necessity of
radicals to solve second degree polynomial equations and build towards degree
five polynomial equations. In eventuality our program shows that there is no
formula for an arbitrary fifth degree polynomial equation that uses analytic
functions, finite field operations, and radicals that reconstructs the roots of
the polynomial from it's coefficients. This theorem was partially completed by
Paolo Ruffini in 1799 and completed by Niels Abel in 1824.
