You're correct, but also forgetting the best part. The ratio between width and length stays the same!!

This specifically is what allows easy up-/downscaling for an A* size.

I guess the key thing actually is that the width of A(n) is the same as the height of A(n+1).

How often do you need to scale up or down a printed document? I don't see how that is useful.

You may want to print multiple pages per sheet.

By hand? Surely it would be faster to click a button in your word processor, which supports letter paper.

Print shops nearly always print multiple copies/multiple pages of a job onto larger sheets and them cut and collate them afterwards, as the print step takes the longest time which includes moving sheets in and starting the print and then stopping the print and moving the result out.

An A1 sheet can fit 4x A3 posters, 8x A4 pages or 16x A5 flyer/booklet pages without any wastage, so all you need is a single A1 printer.

Just like the US paper sizes:

ANSI A == 8.5 x 11 inches (letter)

ANSI B == 11 x 17 inches

ANSI C == 17 x 22 inches

ANSI D == 22 x 34 inches, etc.

There are additional sizes frequently used in the US too: business card, legal, half letter, and specialized sizes for architecture.

11/8.5 = 22/17 = 44/34 = 1.29

17/11 = 34/22 = 1.55

These have the property that they alternate aspect ratios every size, so you have to go up two sizes (4x area) to get back to the original aspect ratio.

Who cares?

I’ve only ever seen letter size paper available in offices in the US whereas almost every office photocopier/printer in UK/EU is stocked with both both A4 and A3. The larger sheets are really nice for sketching diagrams.

11x17 printer trays were common for engineering use before we got decent high resolution monitors and most work process became paperless.

9 x 12 inches and 11 x 14 inches are standard in art paper in the US. As are 5 x 7 and 8 x 10.

The first one, 9 x 12, happens to also be “ARCH A” but I haven’t seen a fancy name for the others.