I just found out by accident that the A0 paper format is designed to have a surface area of 1 m²! An A4 sheet is obtained by cutting an A0 sheet in half 4 times, giving a surface area of 1/16 m².
It came up while playing with formulas to price artworks based on their dimensions. I was using sqrt(height * width) to obtain the side length of the equivalent square and I was surprised to get a round number for sqrt(21 * 29.7).
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@mjambon Each sheet is half the size of the previous. So A1 is half A0, and so on.. so 1/2^N where N is the number in a A series is the relative area to A0.
Similarly B series is half way between the B series. So an A4 is half way between A4 and A5.
@freemo I knew about the height:width ratio being constant at sqrt(2) but didn't know about the surface area considerations.
@mjambon Its actually designed that way for book-making purposes.
A3 sheets used to make a book result in A4 pages that are of the correct ratio still.
@freemo for practical reasons, I reluctantly settled on foot/inch-based formats for my paintings: 18:24 and 24:36 (inches:inches). It doubles the surface area but doesn't preserve the aspect ratio (3:4 vs. 2:3). It's not too bad because if I double the surface area again, I'm back to 36:48 = 3:4. So instead of being always 1/sqrt(2), it alternates between 3:4 and 2:3.
It matters to me when dividing a 4 ft by 8 ft plywood panel without wasting too much.
@mjambon In art usuaing various aspect ratios is very much the norm and important for artistic expression. We only use the ratio we do with books because of the nuances i mentioned earlier in the construction of books and how that specific aspect ratio is halvable while preserving the ratio, which is needed to make books out of paper.
@mjambon I dunno ive seen quite a few ovals, but I agree they arent the norm. It seems to depend on time period. Most of the art, particularly photos, that are oval seem to date to like 100 years back.