I just found out by accident that the A0 paper format is designed to have a surface area of 1 mยฒ! An A4 sheet is obtained by cutting an A0 sheet in half 4 times, giving a surface area of 1/16 mยฒ.

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.

@freemo yes, but not really considering that panels could easily be cut into shapes other than rectangles. Even ovals are relatively rare. Original shapes tend to be distracting and get reclassified into "wall art between painting and sculpture".

@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.

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