Considering a medium creature, with 5ft of reach, wielding a reach weapon such as a longspear.
By the rules:
With a typical reach weapon, you can strike opponents 10 feet away, but you can’t strike adjacent foes (those within 5 feet).
Squares within 5 feet would be all adjacent squares to the creature, including diagonal ones (first diagonal being counted at 5ft).
It appears clear that the weapon will allow attacks into four squares: those 5ft away from the creature in the north, east, south and west directions. They are 2 squares away in a straight line, thus 10ft away, within reach.
But now, what about the squares diagonally away, beyond 5ft, north-east, south-east, south-west and north-west of the creature? According to the rules, the second square of a diagonal line is considered 15ft away when it comes to movement. Does this also apply to attack distances?
Also, what about squares reachable by going diagonally once, then straight up/down/left/right? This would usually count at 10ft of movement, so are they attackable?
Here’s a diagram:
??x?? ?...? x.C.x ?...? ??x??
C is the creature, dots are where I assume you cannot attack, Xs are where I assume you can attack and question marks are where I’m not sure you can.
The Case of the Missing AOO
I’ve come across an interesting point on the Paizo forums. If you are in one of the far corners and you consider these not threatened, then you can diagonally move towards the character and never provoke an AOO (that is, per RAW)… and yet, logically, a threatened area should make an uninterrupted circle around the creature. This may explain why 3.5 made an exception out of this.