## February 2008 Archives

## Mon Feb 11 20:40:01 CST 2008

### Math in monitor resolutions

Most people never think about it, but there's a bit of math that goes into your options for a monitor resolution.
Standard monitors use a 4:3 aspect ratio.
This means that for every 4 inches wide, it will be 3 inches tall.
Widescreen monitors are usually 16:9.
Further reading: Aspect Ratio on Wikipedia

If you wanted to measure dpi, you might use the Pythagorean Theorem to find how many pixels your monitor has from corner to corner and divide this by the number of inches. (Diagonal inches are the measurement used to sell monitors.) About 90 dpi is average: while a higher dpi produces a more crisp image, a smaller number is easier on your eyes. Normally, the smallest standard resolution is 640x480, followed by 800x600 then 1024x768. These have been common for quite a while and most computers can manage much more these days, but 1024x768 on a 17" monitor is still standard.

Have you ever wondered where the numbers we use for standard resolutions come from? I could be wrong, but if you figured out the dpi for a 640x480 screen, you may have noticed that the diagonal measurement was 800 pixels.

It seems that in A^2 + B^2 = C^2, our old C becomes the new A. This doesn't continue, sadly. You would expect the next resolution to be 1000x750, but 1024x768 is prettier in binary. (10000000000x1100000000) It also makes better use of video memory address space, but I'm sure that's a side effect. Besides, 1024 is pretty much the same as 1000 anyway, right? That's what hard drive manufacturers have been telling us for years.

If we continue, we'll see that the next logical resolution would be 1280x960, but most systems skip that and go to 1280x1024, giving you a more square 5:4 ratio. A square monitor would give you more viewing space per diagonal inch, but if you want to watch anything in widescreen format it doesn't help at all. Instead, you get thicker black bars at the top and bottom of your screen.

Speaking of widescreen, the standard format for movies tends to be 16:9. If you were playing around with figuring out the diagonals, you might have noticed that our 4:3 makes a textbook Pythagorean triangle: 4x3 with a diagonal of 5. While you were doing the math you might have noticed that your A^2 and B^2 came out to 16 and 9. That's right. The widescreen aspect ratio can be found by squaring the numbers in the standard,

If you wanted to measure dpi, you might use the Pythagorean Theorem to find how many pixels your monitor has from corner to corner and divide this by the number of inches. (Diagonal inches are the measurement used to sell monitors.) About 90 dpi is average: while a higher dpi produces a more crisp image, a smaller number is easier on your eyes. Normally, the smallest standard resolution is 640x480, followed by 800x600 then 1024x768. These have been common for quite a while and most computers can manage much more these days, but 1024x768 on a 17" monitor is still standard.

Have you ever wondered where the numbers we use for standard resolutions come from? I could be wrong, but if you figured out the dpi for a 640x480 screen, you may have noticed that the diagonal measurement was 800 pixels.

`sqrt(640^2 + 480^2) = 800`

It seems that in A^2 + B^2 = C^2, our old C becomes the new A. This doesn't continue, sadly. You would expect the next resolution to be 1000x750, but 1024x768 is prettier in binary. (10000000000x1100000000) It also makes better use of video memory address space, but I'm sure that's a side effect. Besides, 1024 is pretty much the same as 1000 anyway, right? That's what hard drive manufacturers have been telling us for years.

If we continue, we'll see that the next logical resolution would be 1280x960, but most systems skip that and go to 1280x1024, giving you a more square 5:4 ratio. A square monitor would give you more viewing space per diagonal inch, but if you want to watch anything in widescreen format it doesn't help at all. Instead, you get thicker black bars at the top and bottom of your screen.

Speaking of widescreen, the standard format for movies tends to be 16:9. If you were playing around with figuring out the diagonals, you might have noticed that our 4:3 makes a textbook Pythagorean triangle: 4x3 with a diagonal of 5. While you were doing the math you might have noticed that your A^2 and B^2 came out to 16 and 9. That's right. The widescreen aspect ratio can be found by squaring the numbers in the standard,

**square**ratio.