Pixel count vs. perceived resolution (sharpness, detail)

"Doubling the resolution of an image isn't as simple as just having twice as many pixels. In fact doubling the resolution of an image requires four times as many pixels (...) This is the square law in action. (...) To double the resolution of a one-megapixel camera, we have to go to four-megapixels -- not two-megapixels. To double the resolution of a three-megapixel camera we have to go to twelve megapixels. To double the resolution of a four-megapixel camera, we'd have to go to no less than sixteen-megapixels.
(...)
This means that, to have DOUBLE the resolution, you have to FOUR TIMES the number of pixels."
 - John Henshall, epi-centre.com


"Small differences in pixel count, between say 5 MP and 8MP, are unimportant because pixel counts are a square function. It's exactly like calculating area or square footage. It only takes a 40% increase in linear dimensions to double the pixel count! Doubling pixel count only increases the real, linear resolution by 40%, which is pretty much invisible.
(...)
One needs at least a doubling of linear [in two directions] resolution or film size to make an obvious improvement. This is the same as quadrupling the megapixels."
 - Ken Rockwell, kenrockwell.com


"Theory predicts there is little resolution difference between a 6 and 8 megapixel camera. To double resolution all other things being equal requires that the pixel count be increased four times as both vertical and horizontal dimensions need to be doubled."
 - Ken Newcombe, kennewcombe.com


"...broadcast television resolution properly refers to the pixel density, the number of pixels per unit distance or area, not total number of pixels. In digital measurement, the display resolution would be given in pixels per inch."
 - Wikipedia "Display resolution" article, editor unknown


Report says iPad 3 display has double linear resolution (headline)
"(...) The iPad 2 display is already impressive and so just imagine what we might see with double the clarity!"
 - Mark Chubb, phonesreview.co.uk


"[New iPad] will have a screen that's twice as sharp as the current iPad, according to some icons hidden in the iBooks application. MacRumors found the icons, and says the resolution on the next iPad will likely be 2048x1546, which is a doubling of the current iPad's resolution."
 - Jay Yarow, businessinsider.com


"...the lil’ MacBook boasts a stunning 2560 x 1600-pixel display that’s twice as sharp as its non-retina brethren [1280x800]."
 - Editorial of thedaily.com


"...necessary to double the resolution and therefore quadruple the number of pixels?"
 - Raymond Soneira, displaymate.com


"With an eye-grabbing 2048- by-1536 pixel resolution at 264 pixels per inch, the new iPad's screen has twice the resolution and four times the number of pixels as its predecessor."
 - Jeff Bertolucci, informationweek.com


"(talking about 3rd generation iPad) ...Twice the resolution and four times the pixels..."
 - Andrew Eisner, retrevo.com