Let’s call the two problem regions “violet” and “cyan”.
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**Violet** is a color that is even further from red and green than blue is. So to make it by mixing red, green, and blue light together, you’d need your red and green pixels to have *negative* brightness, which isn’t possible.
We could build computer screens that mixed red, green, and violet light together instead of red, green, and blue light, but our eyes aren’t very sensitive to violet light and so the violet pixels would have to be *very* bright. And violet is already the highest-energy color. You don’t want your computer screen to be able to sunburn or blind you.
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Meanwhile, **cyan** is a color in between green and blue. You might think: no problem, just create it by mixing green light and blue light. The trouble is that the color green is actually very close to the color red, so as you’re adding green light into the mixture, a bunch of redness is going to get in there too. So when we try to display cyan, instead of getting a mixture of green and blue (which would appear to our eyes as the color cyan), we end up with a mixture of green, blue, and red (which therefore looks closer to the color white than the color cyan would).
If we built computer screens that mixed red, cyan, and blue pixels together instead of red, green, and blue pixels, we’d just shift the problem over to the green range: we’d be trying to represent green as a mixture of red and cyan, but as we added the cyan some blueness would get in there too.
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The problem *could* be fixed by having more than three colors of pixel. For example, the “hexachrome” printing system uses both green ink *and* cyan ink. But on computer screens (unlike in printing), extra pixel colors comes at the expense of resolution: if you can fit 1000 tricolor dots per inch, you’ll only be able to fit 500 hexacolor dots per inch. So it’s generally not worth it.
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