Very basic geometry problem, in which I discover that a 32-inch display with a pixel density of 218 pixels/inch (to match Apple displays) requires 6108 x 3436 pixels.
An 8k display would be 40 inches.
h = 32,
218 = p / x,
c = 16/9 y,
x = h cos(t),
y = h sin(t),
h^2 = x^2 + y^2,
90 = t + s,
x > 0, y > 0, h > 0