I returned from summer vacation with a large number of pictures which I am editing. Which leads to a difficult decision. When cropping the pictures, what aspect ratio do I chose for the images? This is not a clear cut question, and any investigation of which aspect ratio to use for cropping pictures leads to much confusion.
Last year, for example I had a beautiful picture of us getting Lei-ed as we arrived in Hawaii. I cropped the picture for a 4 x 6 print (aspect ratio 1.5) and then deciding that it made such a good picture, printed it on a 5 x 7 (AR 1.4) only to discover that the printer chopped off the tops of our heads. Looking further I see that it would get other results if I had tried to print an 8.5 x 11 (AR 1.294...) or a 11 x 17 (AR 1.545...) or a 13 x 19 (AR 1.461...). Fortunately the last two choices are moot because my printer cannot handle theses sized sheets.
There is more. I take a group of pictures and put them on a DVD that we can watch on TV. 60 pictures at 6 seconds each with a sound track will make a high energy 6 minute video of our vacation. However, this creates more aspect ratio choices. Currently TV's are changing their aspect ratio from 4 x 3 (AR 1.333...) to 16 x 9 (1.777...). (And why has the convention changed to putting the larger number first?) In practice TV's are even more difficult as they naturally chop off some lines at the top and bottom of the picture so that a video of still images introduces even more uncertainty when deciding how to crop the images.
If we want to see the whole image in the video, we can look at it on a computer monitor which does not lose scan lines from the top and bottom and will scale everything to fit. But there is a problem even in the logical world of computers. Most of the standard display settings have an aspect ratio of 1.333... (800 x 600, 1024 x 768, 1600 x 1200) however the majority of computer displays sold today are LCD panels at 1280 x 1024 (AR 1.25).
More confusing yet, the display size of 1280 x 768 (AR 1.666...) is becoming popular in both laptops that can be used for watching DVD's on long flights and with LCD TV's where the aspect ratio seems to match what is shown on a 16 x 9 TV even although 1.66... is not 1.77...
There is a lot more to aspect ratio and it only gets worse. For example, the above discussion assumed that the pixels were square which they do not need to be. I have some ideas on what can be done which will have to wait until another time.