There's a generalization of this problem where we consider the set of all lines between (a, 0) and (0, b) with ||(a, b)||_p = 1 as in the Lp norm; and ask, wh

There's a generalization of this problem where we consider the set of all lines between (a, 0) and (0, b) with ||(a, b)||_p = 1 as in the Lp norm; and ask, what curve is produced (as their boundary) ? And the answer has the nice form: The set of points (x,y) which satisfy ||(x, y)||_q = 1 where q = p / (p+1) [which can be written as 1/q - 1/p = 1.] This is written up as the solution to a puzzle here: http://fridaypuzzl.es/?p=187 http://fridaypuzzl.es/?p=187 and if you love puzzles, try to forget what you just read, and here is the puzzle: http://fridaypuzzl.es/?p=180 http://fridaypuzzl.es/?p=180