[apalmer]

The mathematics seem valid to me but the underlying concept of 'knights are weird' just doesnt ring true.

Knights move precisely the way they do because there whole concept is to be able to threaten any other piece without being threatened.

The knights movement is precisely designed to e the simplest movement possible that can fulfill this roll.

The knights ability to jump over pieces comes from the fact that there are always two ways for the knight to get to a square so no one piece can block a knight... I do understand that in theory 2 pieces could block a knight but that's the justification for its magical jumping ability.

[lemoing]

When I referred to knights as weird, I was thinking more of how their movement patterns are incongruous with rooks/bishops/queens that move in a straight line but are blocked by pieces in the way. Their weirdness is what makes them useful (uniqueness may have been a better word).

I liked the way another commenter described it below: knights can move to the closest squares other pieces can't move to.