XXXXXXX In 1958 the Lego patent was filed, and granted in 1961 with 5mm bricks and 3mm studs at its core. I've mention many times in this book how LED lights fit snugly in them. My extensive research has not come up with a definitive answer and this short appendix is an opinion on why that may be.
An LED is typically 1mm2 so the choice of 3mm or 5mm casings is something that is probably down to a personal choice, or tooling options at the time.
The same may be so of the Lego pieces, there is no special reason as to why the dimensions of the bricks and the studs are of the size they are, outside of them being whole numbers within the metric system.
The imperial system of the time sheds even less light on the matter, as it was far from even numbers.
Of interest to me is that they are all Fibonacci numbers, being the sequence of numbers based on the sum of the two that proceed it: 1,1,2,3,5,8,13 and so on. The golden ratio, the ratio of perfection and beauty as it has been called over time.
[Ratio Pic on Graph Paper] [or lego]