This comes down to understanding how logarithms work. Specifically in photography, the log base-2 of a doubling ratio equates to a difference of 1 stop.
We use logarithms to reduce repeated multiplication and division by growth factors to simpler linear addition or subtraction of stop values. If you are familiar with the decibel scale, this is the same ...
As you know, cameras and other optical applications frequently use the f-stop system. The focal ratio (f/#) set in common usage is:
1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 -22 -32 -45 -64
The f-number set is grounded on the geometry of circles. The f/# is obtained by dividing the focal length by the working diameter of the aperture. The resulting ratio ...
Why are not taken the real Area increments of 1.5, 1.33, 1.66 using the radius √(3/2), √(4/3), √(5/3) as the real fractional stops of +1/2EV; +1/3EV; +2/3EV?
Because of addition property.
Surely, you would like adding +1/2EV twice to produce +1EV which means 2*light.
Now, if +1/2EV was 1.5*light, then +1EV would be 2.25*light.