This can be interpreted as, which is larger, the ratio of the area of a
circle to its circumscribed square, or the area of a square to its
circumscribed circle? In 2 dimensions, these ratios are pi/4 and 2/pi
respectively, so a round peg fits better in a square hole than a square
peg fits into a round hole. However, this result is true only in
dimensions less than 9. For n greater than or equal to 9 the
n-dimensional unit cube fits more closely into the n-dimensional unit
sphere than the other way round.
