While doing a landscaping project in our backyard a few months ago, I dug up an old flask-shaped bottle. In my research to find its origin, I came across this site (let me presume to share your surprise that the U.S. government’s Bureau of Land Management has a great resource on bottle shapes and sizes): http://www.blm.gov/historic_bottles/liquor.htm
The flask shape is definitely used to enhance portability on one’s person.
And the fifth is too big for that, whatever shape (so might as well make it round or square), while the mini is meant to be a miniature of the fifth, so it mimics its shape.
What may be more amazing is that someone’s perfectly obscure question is answered so forthrightly in such a short time on this bbs, and with the help of the US Govt to boot. Truly wonderful.