Let's take a look at the mathematics behind An paper sizing.
The aspect ratio is r = w/h where h is the longer side.
Now you want e.g. A1 to be half of A0, so the aspect ratio is r=(0.5*h)/w
We have the equation r = w/h = 0.5*h/w = 0.5/r or r^2 = 0.5
Then r is simply square root of 0.5 or in other words 0.70711.
Thus, the width (shorter side) is 0.70711 ...
Cameras of that era accepted film that was slightly larger than the delivered prints. Work was done in a dark-room. Since both the camera film and the print paper were sensitive only to violet and blue light, work was performed under quite bright red light. Red light is void of violet and blue.
The film was immersed in a series of chemicals and the results ...
Your phone will not generate images with a pixel density of 72ppi... it will generate images with x/y pixel dimensions. What that means in terms of pixels per inch depends on how large it is printed/displayed. E.g. if you use a phone with a 12MP sensor that generates an image of 4000 pixels wide, and you printed that image at 4" wide, it would have a pixel ...
Usually, it is recommended to print photos at 300dpi (= dots per inch, which is the print equivalent to ppi, as printer cannot print pixels but dots). However, if you simply set the pixel density to 300dpi, it might not change anything if the original photo isn't large enough.
You can determine the maximum print size at 300dpi from the photo's dimensions. ...
Because the standard is based on the square root of two — an irrational number — but each size is rounded to the nearest whole millimeter.
The standard also allows for slight variation from the nominal number.
In both theory and most practical use, A1 is exactly double A2. If you need precision beyond that, you should cut your own paper.