There is more to the square than meets the eye. We think that calculating its area is a relatively simple thing, but with some specific parameters, it becomes a challenge that can lead us to playing with different ways of looking at counting numbers, proofs, and maybe even the imaginary! What can we learn about this regular shape when we break free from the grid and give it the attention it deserves?

Note - Circle Prerequisites:
(1) Knowledge of square numbers
(2) Has not explored modular arithmetic in depth