Helpful chart for choosing TV size/resolution

[U4K61]

Originally Posted by ALLIANCE68

1080p NEEDS SCREEN SIZE TO MATCH
Think of it this way. your tv is graph paper.
720p is 1" squares, just to make it easy.
1080p is 1/2" squares double the resolution.

Squares and Viewing Distance:

720p is about 1,000,000 pixels and 1080p ~2,000,000, so 1080p is 2x over 720p. 1/2 +1/2 = 1 in a linear realtionship, as in a number line, which are powers of 1. But we are dealing with an area which is a power of 2. So there would actually be four 1/2" squares fitting inside 1" squares on the graph paper, suggesting 1080p is 4x over 720p, which it is not. Look at the image below of a 4X4 image upscaled to 8X8. You can also see why I would rather convert 480p to 960p with black bars on all 4 sides of the image rather then filling entire screen of a 1080p set.

Square Numbers
The Number Line
Cartesian Coordinates

To get two equal squares to exactly fill the area of a larger square, we have the formula for doubling a square with side of length 'a' for a square of length 'x': x^2 = 2a^2

However, the idea of squares is interesting. If you are at some optimum viewing distance n from your square pixel 16:9 1080p set and cut that distance to n/2, you would need a set with 4k resolution. n/4 would be 8k. The amount of information you can see goes down when you increase distance, and goes up the when you dicrease distance, following the point-source Inverse-Square Law



Viewing Distance Chart
Visible Resolution Limits (photobucket.com)
Viewing Distance Thread

See also the Delian Problem, Doubling the Cube.

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