I don't use the "arms length rule", but the "perfect triangle rule", which results in an immersive but comfortable 60 degrees field of view, so little or no head-movement is needed.
The rule puts the screen at ca 87% of its width. For a typical 24 inch FullHD monitor this results in 46cm and its pixels will be almost invisible. Depending on your taste or monitor one can sit a bit closer of farther.
The rule explained: imagine a perfect triangle between your eyes and the sides of the screen. Now the distance of each side to the eye is the same as the width of the screen, and the monitor is at 86.6% of its width in front of you.
The intuition behind the rule is simple: if you get closer, the middle of the screen will seem to get closer faster than the distance to the sides. The differences in distance become larger and this means your eyes have to work more. Likewise unnecessary distance means pixels become smaller and harder to read.
For those with glasses, the depth of view limits how close you can be to the screen, while still having a sharp view of the sides. Don't sit too close. Good glasses permit a 60 degrees field of view (and not much more), so be sure to buy them with the strength that allows you to sit at ~87% width (as the closest you can get). With plastic glasses you need to sit a bit further away as they typically have a narrower field of view.