wintersolstice wrote:[...]5) uncomfirmed: the sausage conjecture states that in 5D and above the comvex hull of any number of hypersheres is smallest when they're arranged in a line (i.e. when the convex hull is a sausage)
This is an old topic, but I just noticed something funny today. The sausage conjecture is currently only proven for dimensions n≥42, even though the conjecture itself is stated for n≥5. In Douglas Adam's "Hitchhiker's Guide to the Galaxy", the answer to "life, the universe, and everything" is (humorously) computed to be 42. Upon which, the baffled protagonists embark on a quest to find out what the question was (since "life, the universe, and everything" isn't really a question
per se). Now, thanks to this forum, we know what the question was: it was "What's the smallest dimension for which the Sausage Conjecture was proven to be true?"