Paper sizes

Those numbers aren't meaningless. They're the weight of a ream (500 sheets) of that paper at 17x22.

I went into a Fedex/Kinko's in the US, to try to print something on A3.

They looked at me as if I had just asked them to sell me a unicorn. They then offered to custom cut a piece of paper for what I'd approximate as several tens of thousands of percent markup.

Yes and no.

Yes, additional sizes address the desire for satisfying the missing in-between sizes.

No, because I'd like to keep it simple and avoid having to do that or even think about it at all.

Basically, with the ANSI sizes you want to satisfy TWO proportions with gradual size changes instead of just ONE proportion with gradual size changes as seen in ISO 216. This is where the discussion cycles back to the utility of 1:√2.

In most offices in the U.S. that I've been in (I say this in a fast and loose fashion), they carry three sizes (with the following typical uses):

(1) ANSI A (US Letter) for standard letters (uses full portrait page) and leaflets (uses one-third landscape page) or booklets (uses half landscape page).

(2) US Legal because there are plenty of legal documents are out there that use US Legal (uses full portrait page). And perhaps as a bonus, but not as frequently seen, US Legal can be folded into small booklets (uses half landscape page). Although, I don't see this happen as much as ANSI A being used for booklets.

(3) ANSI B (Ledger/Tabloid) because it can be great for spreadsheets and folded to US Letter sized pages. Either for collapsing the spreadsheet or for making booklets with US Letter sized pages (uses half landscape page).

Now, yes, I did not mention all uses. I merely mentioned what I have frequently seen used based on my experience. But one of the key take-away points for the "common-use/general-purpose" ANSI A and ANSI B paper sheets is the notion of folding the paper in half to form a booklet.

You don't see many offices carrying ANSI C (17"x22"), which is the next step up from ANSI A maintaining the same proportion. (So availability of this is considered unlikely in this context.)

Of the three, perhaps US Legal can stand alone because it offers a significantly relevant special situation proportion. So, we'll set US Legal aside for now.

And so, you get usage of Half US Letter (1.5454…), Full US Letter (1.2941…), Half Tabloid (which is just US Letter, 1.2941…), Full Tabloid (1.5454…). So, you'll get an oscillation of two distinct proportions with paper that doesn't use 1:√2, and in the case of ANSI A through ANSI E, you get the 1.5454… and 1.2941… oscillation.

Now, if you had ISO 216 sized paper, all of the proportions would be the same no matter what, and it becomes very easy to choose between paper and half-paper sizes because they all work alike with regard to their proportions.

However, with the oscillating ratios, you have to choose which one you're targeting and be sure of it, because the next larger (or next smaller) size is significantly different.

Now, more in-between sizes could solve this, but that also means you'd probably end up carrying around yet another paper size because of it. If you simplify things by getting rid of the dual-proportions and have a unified proportion instead, then the added frustration from the differing layout proportions go away instead of trying to address that with another paper size for something in-between.

So, to parallel the Half US Letter (feels like an oddball that is basically super small Tabloid, 1.5454…), Full US Letter (1.2941…), Half Tabloid (is just Letter, 1.2941…), Full Tabloid (1.5454…):

Half A4 (is just A5, 1.4142…), Full A4 (1.4142…), Half A3 (is just A4, 1.4142…), and Full A3 (1.4142…).

With the layout for Half US Letter, your next proportional step-up is Full Tabloid. (Huge jump!) Or from Tabloid, your next proportional step-down is Half US Letter (Really small!) You could have an in-between size to satisfy it, but it seems excessive when you could have just had used the 1:√2 proportion to begin with and not worry about any of those additional considerations.

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Saying it another way...

Where, ½·x signifies folding a sheet for purpose as a booklet, and the paper that satisfies that requirement is mentioned inside the cell.

Dealing with only our "letter" size (1) and "tabloid" size (2) sheets that we have in our office, we get the following:

    ANSI    | ½·1 | 1·1 | ½·2 | 1·2 |
            +—————+—————+—————+—————+
    1.2941… | :(  |  A  |  B  | :(  |
            |—————|—————|—————|—————|
    1.5454… |  A  | :(  | :(  |  B  |
            |_____|_____|_____|_____|


    ISO 216 | ½·1 | 1·1 | ½·2 | 1·2 |
            +—————+—————+—————+—————+
    1.4142… | A4  | A4  | A3  | A3  |
            |_____|_____|_____|_____|

With ANSI:

    We don’t have a “half size” booklet with 1.2941… proportions.
    We don’t have a “full size” sheet with 1.5454… proportions.
    We don’t have a “full size” booklet with 1.5454… proportions.
    We don’t have a “double size” sheet with 1.2941… proportions.

With ISO 216:

    We have our “half size” booklet in all our proportions.
    We have our “full size” sheet in all our proportions.
    We have our “full size” booklet in all our proportions. 
    We have our “double size” sheet in all our proportions. 
    (Because we only have one proportion to deal with, 
    there’s no bothering to deal with dual proportions.)

That's four frowning faces (missing solutions for that proportion) on the ANSI side.

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If we were to expand on this beyond the "two typical sizes found in the office" scenario, we get the following:

    ANSI    | ½·1 | 1·1 | ½·2 | 1·2 | ½·4 | 1·4 | ½·8 | 1·8 | ½·16 | 1·16 |
            +—————+—————+—————+—————+—————+—————+—————+—————+——————+——————|
    1.2941… | :(  |  A  |  B  | :(  | :(  |  C  |  D  | :(  |  :(  |  E   |
            |—————|—————|—————|—————|—————|—————|—————|—————+——————+——————|
    1.5454… |  A  | :(  | :(  |  B  |  C  | :(  | :(  |  D  |  E   |  :(  |
            |_____|_____|_____|_____|_____|_____|_____|_____|______|______|


    ISO 216 | ½·1 | 1·1 | ½·2 | 1·2 | ½·4 | 1·4 | ½·8 | 1·8 | ½·16 | 1·16 |
            +—————+—————+—————+—————+—————+—————+—————+—————+——————+——————|
    1.4142… | A4  | A4  | A3  | A3  | A2  | A2  | A1  | A1  | A0   | A0   |
            |_____|_____|_____|_____|_____|_____|_____|_____|______|______|

That's 10 frowning faces on the ANSI side, and no frowns on the ISO side. The ISO side inherently avoids the frowning face scenario.

Yes, you could add on another set of sizes to address the missing proportions on the ANSI side. But, that's inelegant and unnecessary if you just went with the ISO way instead.

Interesting. I always thought base 16 was the only suitable number system. Base 2 is the only justifiable one, since base 1 is not much fun. Squaring base 2 twice to get a fair amount of information in a single column seems to just make sense. What are the downsides of 16?

Yeah, funny how this video was on Reddit's frontpage a few days ago, and this dude just happens to write a blog post about it without even mentioning the video.