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27” Retina math

Reader Adam Lacy sent this via email, reprinted here with permission:

I was reading an article about the new 84” Toshiba 4K TV and it got me thinking about how 4K relates to Retina Display PPIs.
I wanted to speculate on the possibilities for the future iMac/Cinema Displays. In doing so I came across some interesting math.

4K = 3840 × 2160

If you work out the PPI for 4K at 27 inches it conveniently comes out to 163 PPI.

That’s pretty close to the 165 PPI for the iPhone 3GS and the speculated iPad Mini.

Apple’s been having this display PPI manufactured for a long time now and I bet they’ve been testing cuts at 26.7 inches (almost 27).

This would be exactly 4K (3840 × 2160), it would be 165 PPI, same as iPhone 3GS/iPad mini, and would also be exactly 1.5 times the size of the current iMac’s resolution of 2560 × 1440. Not doubled, but I think that matters less for OS X.

This would easily meet some of the Retina Display requirement charts. And would probably work nicely with pixel doubling 1080p video content for display.

Not bad. Not bad at all.

I did some measurements myself: I sit about 24” away from my 30” desktop monitor. If I sat approximately as close to a 26.7” Retina Display, the effective pixel size is similar to the iPad 3 at my viewing distance from it, too. It would barely qualify as “Retina”, but if it had a scaling mode to give me the same space as 2560 × 1440 (much like the Retina MacBook Pro’s simulated 1680 × 1050 and 1920 × 1200 modes), I’d take it.

By the time Thunderbolt is fast enough to send 4K video (some have speculated that this will come with Thunderbolt 1.2 in 2014) and GPUs are fast enough to render the interpolated modes without significant lag, I bet it’ll be surprisingly affordable to manufacture such a panel.