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Pixels, Dots and Resolution
The image that is displayed on the monitor is made up of a gridwork of horizontal and vertical dots called pixels. The number of pixels that can be displayed on the screen at one time is normally called the resolution of the image (or screen) and is expressed as a pair of numbers such as 640x480. More explanation on pixels and resolution can be found in this section on video cards.
While the pixel is the smallest element of a video image, it is not the smallest element of a monitor's screen. Since each pixel on a color display must be made up of three separate colors, there are in fact smaller red, green and blue dots on the surface of the CRT that make up the image. The term dot is used to refer to these small elements that make up the displayed image on the screen.
In order to use different resolutions on a monitor, the monitor must be able to support automatic changing of resolution modes. Originally, monitors were fixed at a particular resolution, but most monitors today are capable of changing their displayed resolution under software control. This lets you use higher or lower resolution depending on the needs of your application.
As time goes on and people do more and more with their PCs, the virtual desktop becomes more and more cramped, and it becomes desirable to be able to use higher resolutions. A higher resolution display lets you see more on your screen at one time and is particularly useful for operating systems like Windows. The maximum resolution that a monitor can display is limited by the size of the monitor and the characteristics of the CRT. In addition, the monitor must have sufficient input bandwidth to allow for refresh of the screen, which becomes more difficult at higher resolutions because there is so much more information being sent to the monitor.
While running the monitor at a higher resolution can be useful, it's important to remember that this makes each pixel on the screen appear smaller as well. Running a high resolution display on a small monitor can be very hard on the eyes. See here for a discussion of screen size issues. Also, for the best picture, the aspect ratio of the monitor should be matched to the aspect ratio of the video signal coming from the video card. Usually, this is 4:3.
Next: Color and Color Depth