Which fits better?

[Buck Mulligan]

Which fits better, a round peg in a square hole or a square peg in a
round hole?

[roy.j...@gmail.com]

the round peg in a square hole fits better than a square peg in a round
hole.

[Buck Mulligan]

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.

[roy.j...@gmail.com]

how did you know that it's true for dimensions 9 and above? what are
their ratios then?

[Buck Mulligan]

work it out.

[joe]

Depends on what you mean by "fits"