In searching for answers to this, 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.
Yes, that is precisely why 3.5e made that exception, and it’s also why Paizo issued an official FAQ that changed Pathfinder’s rules to add the same exception, as @caps reports in this fine answer that you should go upvote.
Thus, a reach weapon can attack the following \$X\$’s from \$C\$:
\begin{array}{c|c}
\phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline
& X & X & X & X & X & \\ \hline
& X & & & & X & \\ \hline
& X & & C & & X & \\ \hline
& X & & & & X & \\ \hline
& X & X & X & X & X & \\ \hline
\\
\end{array}
Before the FAQ change
However, the FAQ entry that caps reports did not exist at the time this question was asked. At that time, you did not get the four corners, and so could only attack these \$X\$’s from \$C\$:
\begin{array}{c|c}
\phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline
& A & X & X & X & & \\ \hline
& X & B & & & X & \\ \hline
& X & & C & & X & \\ \hline
& X & & & & X & \\ \hline
& & X & X & X & & \\ \hline
\\
\end{array}
Here, it would appear that someone could step from \$A\$ to \$B\$ to avoid an attack of opportunity altogether. However, even before the FAQ just changed this to be like 3.5e, the developers at Paizo had ...for lack of a better word, we’ll call it a clarification, though it honestly just confused me more. From an earlier FAQ:
Can you or can you not attack diagonally at a distance of 2x squares (15'=10' exception) with a reach weapon?
James Jacobs: Nope. A reach weapon gives a specific extension to your reach. When you count out squares, since every other square is doubled when you count diagonally, that means that there’ll be corners where you can’t reach.
Sean K. Reynolds: It's an artifact of the grid. The closest the rules come to addressing this is in Large, Huge, Gargantuan, and Colossal Creatures, which says:
Unlike when someone uses a reach weapon, a creature with greater than normal natural reach (more than 5 feet) still threatens squares adjacent to it. A creature with greater than normal natural reach usually gets an attack of opportunity against you if you approach it, because you must enter and move within the range of its reach before you can attack it.
So just because the grid has a square for "15 feet away" and a square for "5 feet away," but no square for "10 feet away," using that corner path doesn't mean you're magically teleporting from 15 feet to 5 feet; you are passing through a 10-foot-radius band around the creature, and therefore you provoke an AOO.
Admittedly it's not clear, and obviously it doesn't have the diagram in the 3E book to provide a non-textual example, but it's supposed to work as I described above.
Basically, the idea was, under the rules at the time, you didn’t threaten 15 ft. away, so you don’t get the corner, but you did threaten 10 ft. away and there’s no way to move from 15 ft. away to 5 ft. away without passing through a point that is 10 ft. away. Thus, someone moving from 15 ft. away on the diagonal to 5 ft. away on the same diagonal was going to provoke even under these rules.
So the enemy at \$A\$ moving to the point marked \$B\$ towards \$C\$ with a reach weapon provoked an attack of opportunity (assuming this isn’t a 5 ft. step of course), because somewhere between \$A\$ and \$B\$, there is a point that is 10 ft. away from \$C\$ that the enemy has to pass through.
Presumably, you would have adjudicated the enemy’s position for the purposes of the attack of opportunity as being \$A\$, though this was never made clear. In this sense, the end result was identical to the 3.5e/post-FAQ version for movement towards you: creatures leaving that corner square to enter a square inside your reach provoked an attack of opportunity as if you threatened that square. You were not eligible to make an attack of opportunity if the enemy performs any other action that provokes from \$A\$, including movement in other directions, because you do not actually threaten it.
This was a headache. Even before the FAQ changed things to match 3.5e, that was precisely what I recommended:
Reach weapons are one of the few fairly-nice things that melee can get. There’s really no need to nerf them. I strongly suggest that you straight-up ignore this nonsense and use the 3.5 rule. The exception to the usual calculation of ranges in the case of reach weapons is weird, but clearly there was a good reason for it: without it, you wind up with this mess.
Towering Mountain of Rage
Right, you want to to propagate Rage effects throughout a tower of creatures. That's... actually kind of interesting. Beast Totem chain grants Pounce and 2 Claw attacks, substantially improving the combat prospects of all creatures in the tower.
Well, the applicable rules are contained here, Pathfinder's Mounted Combat Rules on PFSRD.
Looking them over, we have some... interesting interactions. For a start, as your Half-Orc mount is not a 'combat-trained mount', you have to make a move action to control him in battle as he becomes frightened. Yes, the condition. No, I am not making this up.
But hopefully we could waive that somewhat ill-considered clause (what about an intelligent animal? ugh) and assume a half-orc with player class levels is 'trained for combat riding'. So, you're looking at a DC 5 check, probably with a -5 since a half-orc is not 'suited to riding', to keep the use of both your hands and 'control him with your knees'.
I'm struggling to contain my giggles as I write this.
A slightly more difficult attack is to 'Fight With A Combat Trained Mount', a DC 10 Ride Check, with again that pesky -5 for being ill-suited as a Mount. With Ride as a Class Skill, though, it's probably pretty easy to make this check, especially with an Exotic Military Saddle.
Note that EACH rider would have to make this check, so 3/4 of the stack if you're going Mammoth->Gorilla->Half-Orc->Gnome. I'm not sure if Gorillas get Ride as a class skill. This is particularly problematic as if the Gorilla gets unseated from the Mammoth... well, actually, both the Half-Orc and the Gnome would get to roll to 'Stay in saddle', actually, which is only a DC 5 check. Presumably the Gorilla could attempt to 'Fast Mount' in his next turn, thus returning the stack bonuses to the Mammoth.
I can't find any rules in the Mounted Combat section or the Ride skill to disallow this.
I also think it would be awesome, and utterly approve of the mobile 'Tower of Rage'. Note that the Entire Stack would act on the Initiative of the gnome ("Your mount acts on your initiative count as you direct it. You move at its speed, but the mount uses its action to move.")
I assume this means that the stack acts on the gnome's initiative, but moves at the Mammoth's speed (and if it charges, they all count as charging). Note, I am unsure if a Small Character with 10' of reach from a spear could actually reach the ground if he was on the back of a half-orc on the back of a gorilla on the back of mammoth. I think he couldn't, actually. Ergo, he should probably multiclass to bard and do some form of 'rage music', because, why not.
There is a catch, however; Ferocious Mount mentions that you must spend an extra round of rage to spread the rage to your mount, which the mounts can't do as they have no rage class ability. Greater Ferocious Mount makes no mention of this, but Rage powers don't activate if the wielder is not in a Rage, SO while you can make a Tower of Mounts, you cannot make all those mounts rage unless each mount in the stack is also a Barbarian.
It's worth noting that if each mount is a Barbarian, they will pass on any continuous Rage powers during the Rage to any Barbarians lower in the stack, potentially making the lowest Barbarian have many many many Rage Powers.
But yes. Unfortunately as is it doesn't work unless all but the lowest 'mount' in the stack are all Barbarians with enough Rage rounds to make this worth doing.
Awakened Cat Barbarian riding a Gnome Barbarian riding an Orc Barbarian/Warchanter with war Drums riding a Minotaur Barbarian riding a Huge-Ass War-Mammoth is essentially 90% of the point of playing Dungeons and Dragons.
In 3.5e they would all be wielding monks, as monks are a manufactured weapon.
Probably it would end up looking a little bit like this;
YOUR LIGHTNING IS ALL I NEED
Best Answer
This means that your Space stat takes on the value of your mount’s Space stat, i.e. 15 ft. Your reach doesn’t change, so in this case you have a 15-ft. space with a 5-ft. reach, so you threaten the 16 squares surrounding the 3×3 square. If you have a reach weapon, you don’t threaten those 16 squares, but do threaten the 20 squares surrounding them. So if \$•\$ is where you are and \$○\$ is a square you threaten,
\begin{array}{c c|c c} { \text{Without reach weapon:} \\ \begin{array}{c|c} ○ & ○ & ○ & ○ & ○ \\ \hline ○ & • & • & • & ○ \\ \hline ○ & • & • & • & ○ \\ \hline ○ & • & • & • & ○ \\ \hline ○ & ○ & ○ & ○ & ○ \\ \end{array} \\ } & \quad & \quad& { \text{With reach weapon:} \\ \begin{array}{c|c} ○ & ○ & ○ & ○ & ○ & ○ & ○ \\ \hline ○ & & & & & & ○ \\ \hline ○ & & • & • & • & & ○ \\ \hline ○ & & • & • & • & & ○ \\ \hline ○ & & • & • & • & & ○ \\ \hline ○ & & & & & & ○ \\ \hline ○ & ○ & ○ & ○ & ○ & ○ & ○ \\ \end{array} } \end{array}
Creatures do not need reach to strike you; in fact, these same diagrams work for them. If they stand on a \$○\$ then they can reach one of the \$•\$ squares, i.e. they can reach you (use the grid that corresponds to whether or not they have a reach weapon; your weapon is irrelevant to their reach). However, since your space is larger, they can actually stand closer to you with a reach weapon and still strike you.
This is all kind of weird and very abstract, but Pathfinder is a pretty abstract game in a lot of ways. This simplification is really just an expansion of the already-quite-abstract grid system where a typical person is said to “take up” a 5-ft. cube (I doubt anyone in the history of Homo sapiens has ever actually been 5 feet broad or wide). Basically, you take up that space because you are constantly moving and this is the area you “control” and can therefore move freely in (read: not require an action, not provoke an attack of opportunity). With a mount, which controls its own space, you are able to move around freely atop the mount and so take advantage of the control over that space that it provides.
But that Pathfinder implements an abstraction does not have to be the end of the story. As HeyICanChan points out, Paizo creative director James Jacobs does not consider the abstractions around mounted combat in general to truly be sufficient, suggesting that
In short, Paizo chose simpler, quicker-to-learn, quicker-to-run abstractions for mounted combat, quite possibly because they were focused on more typical cases and didn’t want to bog the system down with special rules for scenarios that may very well not come up in the majority of games (since most riders are just one size category smaller than their mount and therefore the abstraction doesn’t really look too weird). You can choose to do differently, especially if your game isn’t going to look like “most” Pathfinder games and smaller creatures riding very big ones is going to be an important part of it.
But be aware that abstractions are powerful and useful, and reducing abstraction thresholds means greater costs in time to learn, time to run, and complexity. Paizo didn’t think those costs were worth it, at least for their idea of “most” Pathfinder games. You might think they are worth it, at least for your game. But don’t ignore the fact that, worth it or not, the costs are still there. You need to think about them while designing any houserule you want to implement.