Chapter 32: Mathematical Chakra Form
"S = 2(ab + bc + ca), V = abh, S = 6a², V = πr²h..."
"If you view everything in the world as cylinders, cones, cubes, cuboids, right triangular prisms, and other three-dimensional shapes, you can develop spatial awareness and gain a better understanding of three-dimensional forms.
"Chakra works the same way. If you can adjust the internal structure of your chakra while performing Shape Transformation based on these principles, you should be able to manipulate chakra with far greater precision, reduce chakra consumption, and increase the power of your ninjutsu.
"Furthermore, by applying concepts such as the effort arm and resistance arm from the principles of levers, you can create a relatively small lever effect within the same ninjutsu. Its power would far exceed that of an ordinary technique..."
Gōenji was bored enough to cry.
Because he couldn't practice ninjutsu or anything else that might attract attention near Iwagakure, all he could do was conduct endless analyses and calculations inside his head.
And then, his thoughts suddenly began racing.
It was as if all the knowledge he had learned before suddenly connected in his mind at the same moment, producing something akin to an epiphany.
Countless mathematical concepts suddenly connected with everything he understood about the chakra system.
A new concept gradually took shape in Gōenji's mind.
Mathematical Chakra Form.
For a long time, Gōenji had been thinking about how he could surpass people like Madara Uchiha as a member of the Uchiha clan who would never be able to awaken the Mangekyō Sharingan.
It was an extremely difficult goal.
At first, he had focused on the various applications of Fire Release and had begun developing a deeper understanding of Nature Transformation.
That had already made him considerably stronger.
And that was an important foundation if he wanted to one day surpass Madara.
Now, this new concept could serve as another piece of the puzzle.
Gōenji temporarily called it Mathematical Chakra Form—the application of mathematical knowledge to Shape Transformation.
Take Minato Namikaze's Rasengan, for example.
In Gōenji's eyes, the Rasengan was essentially an application of the mathematical principles behind vortices—a concrete manifestation of a free vortex.
Chakra simply amplified the resulting force, allowing it to reach an astonishing level of power.
Of course, Minato had developed the Rasengan based on the Tailed Beast Bomb, so Gōenji had no idea whether he had actually used mathematical formulas when creating it.
Perhaps he had.
Minato had been a genius from childhood. He must have learned an enormous amount of knowledge, or perhaps he had consulted countless mathematical concepts while researching the Rasengan.
Or maybe his talent was simply monstrous enough that his understanding of chakra alone allowed him to derive the Rasengan from the Tailed Beast Bomb.
Gōenji couldn't say for certain.
But it didn't matter.
He was extremely satisfied with this new concept.
His goal of surpassing the Mangekyō Sharingan had just taken another step forward.
Take the Great Fireball Technique.
If an ordinary Great Fireball merely changed its shape and nature, its power would remain within the normal range.
But if this new concept were incorporated into it—combining mathematical principles governing leverage and arranging chakra in different structures to exploit the mechanical advantages created by those shapes—the same ninjutsu could reach an entirely different level of power.
"I'm a genius!"
Gōenji didn't actually use any ninjutsu.
Instead, he simply formed a ball of chakra in his hand.
The chakra continuously twisted and changed shape, sometimes becoming a bird, sometimes another animal.
However, none of the forms were particularly refined.
Without powerful chakra control, this was impossible.
Chakra wouldn't automatically arrange itself into whatever shape he wanted.
He had to control every part of it himself.
Therefore, although he couldn't practice other ninjutsu that might create too much commotion, he could still use this method to train his chakra control.
He had to prepare himself now.
The thought of eventually being able to unleash ten times the power with only a fraction of his chakra made Gōenji extremely excited.
Wouldn't that essentially amount to an increase in his effective chakra reserves?
Even as an Uchiha, he would eventually run into problems related to chakra capacity.
As for the mission and everything else...
Who cared?
Right now, he was immersed in a sea of knowledge.
Once he finished mastering this new concept, he would return triumphantly like a king.
...
Just as Gōenji was feeling pleased with himself, the situation on the battlefield was changing by the second.
Iwagakure's combat strength remained remarkably strong, placing enormous pressure on Konoha's forces.
Konoha had even been forced to deploy Namikaze Minato's unit, the Ino–Shika–Chō trio, members of the Hyūga clan, and other powerful shinobi to intercept Iwagakure's forces.
Although Minato's reputation was already immense, he couldn't gain much of an advantage against Iwagakure's enormous army.
On the Kirigakure front, another young genius from Konoha began making a name for himself.
Kirigakure was an isolated village across the sea. No one knew exactly what Hiruzen Sarutobi was thinking, but Kirigakure's primary opponents were the Uchiha forces stationed on the battlefield.
Large numbers of Uchiha were active on the battlefield.
And it was during this war that Uchiha Shisui rose to prominence.
The reputation of Shisui the Teleporter spread throughout the shinobi world.
His extraordinary Body Flicker Technique was even praised by Kirigakure's shinobi as being comparable to Namikaze Minato's.
His genjutsu, in particular, caused endless headaches for the shinobi of the Mist.
At first, Kirigakure hadn't committed too many forces to the conflict, and this made them realize that their strategy had been mistaken.
Facing the Uchiha clan's powerful Fire Release, Kirigakure should have held an advantage as a village renowned for Water Release.
Yet the Uchiha were simply too powerful.
Even while suffering an elemental disadvantage, they still led their respective units in intercepting Kirigakure's forces.
As for the Sunagakure front...
The consequences of the Third Kazekage's disappearance continued to spread.
After the Fourth Kazekage, Rasa, took office, he did not join forces with the other villages to launch a full-scale assault on Konoha.
Instead, he stationed troops along the border to harass Konoha.
As long as Konoha didn't mobilize its forces to attack another village, Sunagakure wouldn't make a move. But the moment Konoha shifted troops elsewhere, Sunagakure would deploy its own forces to tie them down.
It wasn't that Sunagakure didn't want to attack.
The problem was that the Third Kazekage had disappeared, the Fourth Kazekage had only recently taken office, and this was not the right time to launch an all-out offensive.
At the same time, Sunagakure had no intention of coordinating with the other villages.
They simply wanted to watch the supposedly strongest Konoha struggle to respond at full strength and slowly exhaust itself.
This cunning strategy caused Konoha endless trouble.
They couldn't fight, but they couldn't refuse to fight either.
If they launched a war against Sunagakure, Konoha didn't have enough troops to deal with them.
If they didn't fight, they couldn't withdraw their forces or redistribute them to attack other villages.
It was a dilemma.
Konoha could only adjust its strategy rapidly, deploying the most suitable forces to contain Sunagakure's army.
Meanwhile, on the Kumogakure front...
The intensity of the fighting between Kumogakure and Konoha had decreased somewhat.
For some reason, however, Kumogakure and Iwagakure had become locked in fierce combat.
The Third Raikage had already personally led his forces to the battlefield and engaged Iwagakure's shinobi.
The fighting was even more intense than the battles between Konoha and the other two villages.
Iwagakure's strength was equally impressive.
They could fight Konoha on one front while simultaneously engaging Kumogakure in a fierce battle on another.
"What?! That bastard, the Third Raikage, actually led his forces deep into our territory?"
In Iwagakure, Ōnoki stared at the intelligence brought by one of his trusted subordinates.
His already prominent red nose seemed to flare with anger as he read the report.
"Does that bastard really think he can underestimate me?"