Digital formats and the K.I.S.S. (1) principle

Certainly due to my scientific background or more simply to my advanced age and my subsequent difficulties to memorise things; when acquiring new knowledge, i need to find some logic to cling to, to find rules or invariants (which human brains and senses are found of).
My point is: Is there a logic behind the progression of digital format standards?
Lets go through it.
720p is the heigth (H) of the 1st common one. Assuming the well known ratio 16/9 applies  here comes the 1280px width 🙂
lets try the 1080p then: H=1080 hence L= 1080/9×16=1920px  🙂 🙂
2K ? must imply 2048 px Heigth…oups 2K is no more the heigth but the width now  🙁
Never mind, H should be 2048×9/16= 1152 . Unlucky again! After the textbook it’s 1556: the ratio has changed 🙁 🙁
What about 4K ? logic returns! (in some way) 4K is 4x2K definition, and not 2 times because the definition is the square of a length…
To be definitely lost, it appears that there are ‘other’ 2K and 4K definitions compliant with the 16/9 ratio… or not!
(1) The KISS principle or Keep It Simple Stupid (2), is a principle of efficiency that has been used in massive collaborative development projects such as Linux Operating System writing.
(2) it has very little to do, even if the perspective is tempting here, with the ‘Kiss me stupid’ A.K.A the ‘Billy Wilder Principle’…