How do you back pedal Pythagorus to get an idea what an 84 inch might be in the real world ?
According to my TV screen comparison spreadsheet an 84 inch 16:9 TV would have a screen about 73 inches wide, 42 in height. If viewing a program in the old 4:3 ratio it would be the equivalent of a ~ 68 inch TV.
84 = (W2+H2)1/2 Doesn't help much unless you know the relationship between W & H.
In the case of HD TV the aspect ratio relates screen width (W) and screen height (H) as 16:9 or 1.78:1 which is independent of screen size. This ratio was a compromise between the old 1.33 AR which was utilized by "standard" TV and dates back all the way to the AR of 35MM film. The 1.78 AR was adopted prior to the flat screens now in wide use and was designed to minimize the cost to manufacture HD vacuum tubes. Since vacuum tube displays have virtually disappeared and the choice was locked in to the technical specifications, we are stuck with 1.78 until the "next big thing" in TV hits the scene (holographic displays?).
Why do I say "stuck"? Because 1.78 does not fit any of the aspect ratios currently in use for motion pictures. Original format movies are 1.33, 1.85 "flat", 2.40 (anamorphic), and 2.35 (Panavision). None of these formats will display with out distortion on a 1.78 AR screen. The answer is either to over-scan the picture and clip the parts that don't fit, or to display some black area at top and bottom and both sides.
Since manufactures are no longer constrained by the economics of manufacturing vacuum tubes their flat screen products do not necessarily follow the 1.78 AR rigidly and therefore calculations based on 16/9 should be considered approximations. OK? so hear goes;
We know that 84=(W2+H2)1/2 and we are guessing the W/H = 16/9 therefore we can say that;
W/H = 1.78 or W = 1.78H further W2 = (1.78H)2 therefore;
84 = ((1.78H)2+H2)1/2
H = 84/((1.782 + 12)1/2
H = 41.14" and W = 1.78H = 73.23"
Assuming AR = 16/9
Proof:
D =(41.142+73.232)1/2
= (1692.4996 + 5362.6329)1/2
= 83.9948"
Regards,
GtG
PS It took a while to shake the cobwebs out but it's pretty much straight algebra.
It's worse than that.....you also have to take the "aspect ratio" into account. Using the diagonal only made sense as long as all TV's had the same aspect ratio.
I wish TV (and monitor) vendors would come into the 21st century and drop the danged diagonal measurement and state the spec as LXWXH. Or at least include that info as well as the diagonal.
I’ve a TV screen about that size. Front projection, that is. Very cheap.
It retracts from the ceiling, and yes, it dominates a whole wall in a fairly large room. It’s super-distracting when it’s not in the ceiling.
But 32 inches used to be huge... and now they seem tiny... so who knows... maybe 52 inches will be considered tiny in the future.