If you divide each brick into four as shown, each of those quarters will have the same proportions as the original brick. We can say without losing generality, that the height of each of these new bricks is 1. If we call the length of each of the mini bricks ‘x’, this value will be the proportion we are seeking.

If we make a Pythagorean triangle in two different ways as shown, their hypotenuses will both be equal to the circle radius R.

R^2 = (2x)^2+3^2 = (3x)^2 + 1^2

4x^2+9 = 9x^2+1

5x^2 = 8

x^2 = 8/5

x = sqrt(8/5) = ~1.265

so the proportion of each brick’s length to its height is ~1.265