Stokes' Theorem relates the macroscopic circulation around a boundary to the microscopic rotation (curl) summed up inside the interior. A classic 2D instance is Green's Theorem:
Left Side: Walking along the edge, summing the wind at your back.
Right Side: Adding up all the tiny "spin" values inside the shape.
Instructions: Select a vector field, then click and drag to draw a closed
loop on the canvas. The loop will automatically close when you release the mouse.
Notice that the red areas indicate positive (counter-clockwise) curl, while blue areas indicate negative (clockwise) curl. When your loop encompasses both, they cancel out!