I would also like to say that I was slightly curious about your use of the
cotangent of 0.3 arcminutes
Seems a bit low a value given the pupil is given as limited to 0.4 arcminutes at best - diffraction limit at optimum pupil dilation (although this is based upon wikipedia which is good but not always 100%).
With black and white alternate lines (each a pixel wide*), a simple spreadsheet I've knocked up tells me that someone that can resolve 1 arcminute (20/20 vision) can't see the lines on a 42" Full HD tv at distances greater than approx. 2meters. At about 3.8 meters the same person can't see the lines on a HD Ready set. In other words at more than 2 meters away then this person, with 20/20 vision, could not see all the detail on a (theoretical**)Full HD tv.
The distances change to 4m(Full HD) and 7.5m (HD Ready) for someone with eyes that can resolve 0.5arcminutes: in other words this person would benefit more from the full HD resolution than the person with 20/20 vision.
The distances change to 2.4m (Full HD) and 4.5m(HD ready) for someone with a 50" screen and 20/20 vision. In other words at more than 2.4m away this person could not see all of the detail on the Full HD tv.
Conclusions: Full HD is a nice to have, but the potential of it is not always realised due to viewing distances and non-perfect eyesight for 42" displays! As for 4k, might be a good idea for very large screens & projected images but a bit over the top for 42" plasma/LCD.
**Not included in the calculation: the fact that the HD source compression algorithms may well limit resolution rather than the display, particularly for scenes with lots of motion? Anyone care to comment as I'm not an expert in this..? Plasmas also dither the information on the screen (search for posts by 'vierrafan' on the plasma forum) to improve perceived colour performance thereby potentially further reducing resolution (LCDs don't do this however). Also there's the motion handling of the display processing to consider which also reduces resolution..
* assumptions: illuminated pixel assumed in spreadsheet to take up 80% of total pixel area.
HD ready pixels assumed to be rectangles (1024x768): ie. hd ready vertical resolution not the same as horizontal.
Maths is similar to this:
theta1 (between 2 pixels) = 2x(Inverse Tan ((1.2xpixel separation/2)/distance to screen)
then compare this value theta1 with theta2, the angle that the given eye is capable of seeing.