Say I import a TIFF, JPEG, or PDF image. How can I quickly determine the original aspect ratio of the image so that I can properly scale its size? I have thus far been unable to find an answer looking through the manual.
ImageDimensions will give you the pixel dimensions of an imported image, from which can calculate the aspect ratio:
img = Import["http://www.eschertile.com/pic/ss-2.jpg"];
If you want to know the aspect ration of the image without importing the image itself, you can use "ImageSize" as last parameter to
N[Divide @@ Reverse@ Import["http://www.eschertile.com/pic/ss-2.jpg", "ImageSize"]]
which gives the same value of
ImageAspectRatio[Import["http://www.eschertile.com/pic/ss-2.jpg"]] // N