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Horizontal and Vertical DPI isn’t the same
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DPI requires knowing the screen size and the resolution
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But one can scale around by adjusting DPI without knowing what the natural DPI is
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Screen DPI is different from the System DPI, which is what we are usually interested in
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Even if EDID (see Adjusting Monitor Brightness in Linux) helps in knowing the physical dimensions, this does not work for a projector (see Colour Systems).