I'm leaning towards replacing my current monitor (an LG) with an Apple Thunderbolt Display. The display would mostly be used with my computer but I'd like to be able to watch TV with in occasionally. I don't see any way of getting input to the display other than via Thunderbolt in the manual. My TV signal arrives via a coaxial cable. How could I get the coax's output onto the display? I'm aware elgato makes a product that could get the signal onto my computer, whose output I could then show on the big display. But is there a configuration that wouldn't require my computer to be in the loop?
How to show TV from a coaxial cable on an Apple Thunderbolt Display
televisionthunderbolt-display
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Your calculation is solid. Everywhere I've seen it 109 PPI (which is probably what you intend with DPI) is what people report for the Thunderbolt Cinema Display:
The TUAW article has this nice picture to catalog various pixels per inch densities:
The linked article above even has a Google-hosted spreadsheet with details on the data behind the table.
I have the same model Mini and have found it to be extremely sensitive to temperature. You're lucky you didn't permanently damage yours by keeping it in a drawer. It needs to be out in the air with good clearance around it so that the fan can draw air through.
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Best Answer
You might consider a TV tuner with HDMI output like this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16815260027
Then an HDMI to Display Port or Mini Display Port (Thunderbolt is backwards compatible with Mini Display Port. Display Port would need an adapter to the Mini variety) like this:
http://forums.macrumors.com/showthread.php?t=962633
Shop around for devices such as these. No idea how well any setup would work, I'd love to hear back how well it works out.