The Equation Perfect Pie

In honor of the serious eats pi day contest we are submitting this equation perfect square pie.  After all, the equation calls for pie squared! 

Step 1 Ingredients

4-5 Cups Tart Apples (combination of Granny Smith and Jona Gold works good)
  Peeled, Cored, and Sliced
Scant 3/4 Cup Sugar
Scant 1/4 Cup Brown Sugar
1 tsp Cinnamon
1 Tbs Lemon Juice
Pinch of Salt
1-2 Tbs Flour
4 Tbs Butter, plus a little extra to dot the filling