Interestingly, the R5 intervals are quite close to the golden ratio (1 : 1.618).
Also, I often wondered whether the US use different preferred numbers for buildings, because everything just feels a little different and out of proportion to me. However, this could also be due to the non-metric system in the US.
The numbers cited in the article are convenient only if the relationship between your units can be expressed with powers of 10.
My biggest petty complaint is with the 8" x 11" (Letter) paper size and related formats like Legal and Ledger. The ratios are all over the place. The European A0/A1/A2/A3/A4/A5/A6 papers all have a ratio of 1 : 1.414 (square root of 2), so two sheets of Ax always fit exactly into one sheet of Ay where y = x - 1.
You know what's worse than having paper sizes with differing aspect ratios? Having different paper sizes by region. The simple fact that if someone in the US sends me their CV and I print it in London, it comes out looking bad (sometimes even sideways, by some bizarre quirk of some rather expensive printers).
I mean, sure, the paper sizes used in engineering in the US have the property that two smaller ones side by side match the next larger size (http://www.engineeringtoolbox.com/drafting-paper-sizes-d_214...) but it's still a pain because it's all denominated in inches. There's no reason for that at all--it's not like there is value in having engineering drawings printed on physical paper with round-inch dimensions--even if the drawings are in inch scale.
So, US people: step up and abandon your paper sizes, because no one else is going to do it.
What's crazy is that if you take the golden ratio, multiply it by 2, substract 1, square the result and finally raise 10 to the power of the inverse of what you obtained, then you get exactly the R5 ratio :)
1.6 is the 5-th root of 10 rounded off. But the 5-th power of the golden ratio is very close to 11, not 10, because 11 is the 5-th Lucas number and L_n = φ^n + (-1/φ)^n.
