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According to https://en.wikipedia.org/wiki/VT05

the VT05 presented the user with an upper-case only ASCII character display of 20 rows by 72 columns.

At first glance this seems a reasonably natural resolution, a little less than the later 80×24, but it feels natural that the very first model should have lower resolution.

But fridge logic: where do the numbers come from? 72×20 = 1440, which is not close to a round number in binary, suggesting that it's not the sheer cost of memory that's the limiting factor. It's also not (or at least, not only) the achievable pixel clock rate; that would limit horizontal resolution but not vertical.

Apparently this terminal used shift registers for its memory, which might be a clue. Did those come in some sort of oddball size that made 72×20 a reasonable fit, somehow?

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    Maybe 72 plus fudge factor for horizontal retrace is a normal size of shift register – OmarL Feb 4 at 18:48
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    Maybe a link back to punched cards, which were nominally 80 characters, but often reserved 8? – Mark Williams Feb 4 at 18:50
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    It is likely the deciding factor was video bandwidth and the characters themselves. I.e. older video screens were likely not a whole lot better than television resolution. They likely pushed it as far as economically feasable and built char. ROMs to match "close to" 80 columns wide. A pica typeface typewriter had 10 characters per inch. Giving an 8.5" page 3/4" margin on each side would leave 7 inches, or 70 characters per line. It would not feel too restricting compared to what people were used to, except for lack of lower case. – RichF Feb 4 at 19:06
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    upper-case only, ASCII, and 72 columns also describes the model 33 Teletype. – Solomon Slow Feb 4 at 20:07
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    I think @SolomonSlow is on to something. Much of what would standardize as "80 columns" was often 72 in practice, early on. Aside from the teletypes, there's also how the standard 80 column punch card had 72 usable columns, if you excluded the identification sequence (card number) on the right. – RETRAC Feb 4 at 21:04
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Several sources around the web repeat the notion that the VT05 was a "drop-in replacement" for the (ASR33) teletype.

For example, on gunkies.org:

The VT05 Alphanumeric Display Terminal (technically, the VT05B, but documentation usually referred to it as the 'VT05') was one of DEC's first video terminals. It supported all the same format control characters as a Teletype, so it was a 'drop in' replacement.

The DEC VT05 manual says something like that: "similar to a teletypewriter".

That being the case, the teletype-compatible 72 character width seems like a good choice.

In actuality, the ASR33 could print 74 columns -- see page 1-15 in this Teletype manual. But it was widely considered to be a 72-column device, perhaps because we were all used to 72 useful columns on a punch card. Indeed, the DEC Small Computer handbook, page 128 for the PDP-8 describes the teletype as having a 'standard' (whatever that means) line length of 72 characters. So there's evidence that DEC treated it as a 72-column device.

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In the 1960s, many major languages such as FORTRAN and COBOL specified a line length of 72 characters. This was largely due to the limitations of the 80 column punch cards with which they had been originally programmed. An IBM punch card used 8 columns for a sequence number, leaving 72 to encode characters. This practical limitation was enshrined in the relevant specifications for the languages.

As such 72 columns of text would have been a reasonable line length for a programming terminal in 1973, able to show any record length that was allowable.

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