We know that some screen's height-to-width ratio of resolution is 4:3, like 800 * 600, 1024 * 768 and 1600 * 1200 but many resolutions are not follow this rule,like 1280 * 800, 1440 * 900 and 1920 * 1200. Why does it happen and can I enumerate the height-to-width ratio of resolution?
Why does it happen?
It happens because people like wide format displays, they like display formats that fit in their pocket.
can I enumerate the height-to-width ratio of resolution?
There's nothing prohibiting you from enumerating whatever you want to enumerate. But why would you want to enumerate the height-to-width (or width-to-height) ratio? Why would you need to do that?
The display is the display. Its height is its height, its width is its width. Is your application going to use the entire display, or will the user have a task bar that occupies part of the display. Is your application going to require full screen, or will your app run in a window, or as a widget on a screen?
And what if a user has a circular or oval display? Are you going to allow your application to be "larger" than the actual display? Will your application allow your user to zoom (scale) and scroll the view over the large canvas?
FOLLOWUP
Q: I just want to know whether there is a standard ratio.
A: In terms of just aspect ratio, yes.
There have been many common "standards" for video display (standard in terms of aspect ratio, resolution, color depth, refresh rate). In the PC era CGA 320x200, VGA 640x480, SVGA 800x600, XGA 1024x768, SXGA 1280x1024. Some users rotate their displays 90 degrees, so its an inverse ratio. Now widescreen laptops and displays, 1280x760, 1366x768, 1600:900, et al.
In cinema (films) 1.85:1 and 2.39:1 are common ratios. In broadcast television NTSC (4x3, 480i) and PAL. Now with digital HD widescreen, the standard is 16:9 (formats 720p, 1080i, 1080p, now up to 4K), and TVs now serving as computer monitors. Throw in zooming, cropping, letter box, stretching, etc.
Now with the tablets, smartphones, native display resolutions all over the board, people rotating them 90 degrees.
Are there standard aspect ratio? Yes, several of them.