The number of pixels is not a measure of resolution. In this context "resolution" defines the ability of an image to resolve detail. To double resolution (i.e. to be able to resolve a pair of lines that are half the distance apart) requires 4 times the number of pixels, because images are 2 dimensional, not 1 dimensional. Although "4k" sounds like it must be 4x better than 1080p (after all, 4000 is 4x 1000 right?), it could just as easily be rewritten as "2160p". For marketing reasons, the promoters of UHD TV (=4k) decided to use the horizontal resolution (4k) rather than the vertical resolution versus earlier HD standards (like 1080p or 720p).
Megapixels is not a particularly useful metric for describing resolution unless you are trying to make a 40% increase in resolving power sound like 200%, which is exactly the game of marketers.
Megapixels is just what it is, is exactly the outcome of resolution.
The size of square A is 2m x 2m, or 4 metres squared.
The size of square B is 4m x 4m or 16 metres squared.
Square B is four times the size of square A.
So If you take that square and you will make each edge 2 times longer, the resolution will be 4 times higher.
The image is 4 times bigger/denser.
[doublepost=1503651024][/doublepost]
The problem is your definition of size: you chose area rather than a linear measure. Thats fair enough if its what is important to you. But lets say we upscale building A from 10x10x20 metres high to 20x20x40 metres high. How much bigger is it now? Double the height? 8 times the volume?
Scientists who define and measure resolution (I'm one of them) use a linear measure to define image resolution (and technically we mean here spatial resolution, not temporal resolution or color resolution, which are separate issues). It is typically specified in line pairs per inch (or mm). With 2160 pixel rows, a 55 inch 4k UHD TV has precisely double the resolution of its 1080p counterpart.
You just added another dimension.
Considering it, it's a completely different dimension of discussion, then.
Maybe you will add sphere next?
Image is flat. The resolution, for example, of a 16 MPX photo and 8 MPX photo can be normally measured and it's significant and straightforward.
The resolution is what it says it is, it is: "1280x720" <-- this whole equation is the resolution, gives you info about aspect, and the outcome of it, is the number of megapixels. A photographer knows, that he can't Photoshop too much on a 0.3 MPX photo, but he knows he can do a lot on a 10+ MP photo.
So that the image will be now 8 MP instead of 2 MP, it's a significant value, 4 times larger than before.