Chapter 97: The Submerged

Ace gently flipped through the parchment scroll, tracing the familiar handwriting. He could sense the turmoil in the heart of the diary’s owner.

When Ace himself discovered the path of the supernatural, he too felt such turmoil, such an inability to restrain himself.

However, everything in the settlement was already telling him that the path of the diary’s owner had likely ended long ago.

“30th August, 29th Year of City Founding, Hail

Why does it always fail!

Why can’t this mysterious pattern that reinforces the Source Power Pattern perfectly align with the Source Power Pattern?

Why are the structures that work on Monster bodies unworkable for me?

There must be something I’ve overlooked. If I carefully examine the combination of these pattern structures, they seem to resemble what a certain mathematician described. Perhaps I should seek help in the northern academic center, Milne.”

“1st March, 30th Year of City Founding, Sunny

I!

Citizen Nicholas, no, Shaman Nicholas!

Finally arrived at the great academic center of the Northern City-States, Milne City State!

Legend says the famous mathematics school, the Pythagoreans, is here. I must find a way to infiltrate them.”

“15th March, 30th Year of City Founding, Sunny

Finally succeeded in infiltrating the Pythagoreans!

My power hasn’t effectively increased for a long time. I hope this place can give me the answer. ‘The ratio of any two line segments can be expressed as the ratio of two integers.’ This statement sounds very simple. I hear this is the cornerstone of the Pythagorean school.

I must delve deeply into learning what integers and fractions are.”

“10th May, 30th Year of City Founding, Light Rain

‘The ratio of any two line segments can be expressed as the ratio of two integers.’ This judgment seems to have a problem! Applying this judgment still prevents me from effectively combining the structure that reinforces the Source Power Pattern. There must be something I’ve overlooked.”

Ace read on. He was momentarily in a trance, as if he had become Nicholas, placed in the academic center of Milne City at that time.

The Pythagorean school was located on a high hill in the south of Milne City. The students of Pythagoras had built an academy here.

One could enter the academy and study mathematics simply by paying one Gold Thales and swearing allegiance to the cornerstone theory of the Pythagoreans: “The ratio of any two line segments can be expressed as the ratio of two integers.”

It was nighttime in the academy. Nicholas’s room.

Nicholas failed again to combine the patterns. He quietly stared at the mysterious patterns dissolving in the air, feeling pain and anxiety.

“The gate to the mysterious world seems to be tightly locked. The key to opening it must be hidden in mathematics. Something must be wrong!”

Nicholas, after a period of foundational mathematical study, already possessed basic mathematical skills. Many mathematical principles could be applied to the understanding of the patterns, which strengthened his confidence.

“I need to go for a walk. The more agitated I am, the less likely I am to solve the problem.”

The moon was bright tonight. Figures walked in twos and threes along the path around the academy lake. Nicholas’s mood slowly improved.

Just then, a young man with gray hair, wearing a cyan robe with a red ribbon, caught his attention.

The young man was squatting on a patch of sand by the lake. Aided by the moonlight, he was drawing something with a small stick.

Nicholas quietly approached. The young man was completely absorbed and did not notice Nicholas. He muttered to himself while drawing and marking on the sand.

Reflected in the moonlight, Nicholas saw the young man drawing a right-angled triangle.

“Just a beginner apprentice,” Nicholas thought. “Everyone in the Pythagorean school knows the Pythagorean theorem: the sum of the squares of the two shorter sides of a right-angled triangle equals the square of the hypotenuse. The most classic example is 32+42=52.”

Nicholas immediately felt bored and prepared to leave.

“The Pythagorean theorem is generalized as a2+b2=c2. Assuming a=1 and b=1. Since a2+b2=c2, then c2=2. So what is c? Practical drawing and measurement also confirm this. So what exactly is c?”

The young man scratched his messy, nest-like gray hair in confusion. He suddenly stood up, almost bumping into Nicholas, who was about to leave.

“I’m sorry, I’m sorry. I didn’t know anyone was behind me.” The young man said flusteredly.

“What did you just say? Say it again!” Nicholas felt a thought spark and roared, grabbing the young man’s collar.

The young man was startled. He said hesitantly, “I didn’t know anyone was behind me.”

“Not that! The other sentence!” Nicholas roared like a maniac.

“I’m sorry!” the young man said with some terror.

“Not that either!” Nicholas continued to roar like a madman.

“What exactly is c?” the young man asked tentatively, nearly in tears.

“That’s the one! Tell me, what exactly is c? Is it an integer or a fraction?” Nicholas inadvertently revealed his somewhat superhuman strength, lifting the young man into the air with one arm.

“I—I don’t know. I think it might be neither a fraction nor an integer!”

Nicholas slowly set the young man down, muttering to himself: “Not a fraction, nor an integer! Not a fraction, nor an integer!”

The young man was terrified by the superhumanly strong Nicholas. Seizing the moment while Nicholas was distracted, he scrambled away and fled.

Nicholas ignored the young man. He squatted on the sand, staring silently at the isosceles right-angled triangle.

In the following days, Nicholas confined himself to his room, performing calculations day and night.

“It’s not just the isosceles right-angled triangle. The ratio of the diagonals of a regular pentagon also cannot be precisely calculated! Although it can be approximated by 0.618, its exact value is neither a fraction nor an integer. Beyond fractions and integers, there is a new kind of number!”

Nicholas walked out of his room, his hair disheveled and his face grimy. He looked up at the night sky. There was no one around.

In the air, Nicholas reconstructed the complex pattern structure according to his newly derived results. As he mentally traced the pattern, the invisible power of nature gathered and pulsed. Nicholas effortlessly drew the reinforced Source Power Pattern in the air!

He guided the power of the pattern toward himself. Natural power surged in. It felt as if a boundary had opened in both his soul and body.

Invisible chains seemed to shatter. Nicholas felt both his body and soul had sublimated. He was completely different from his past self!

“Yes! This is that power! The mysterious gate of the supernatural world did not stop me after all, for I now firmly grasp the key to the gate—and that key is Mathematics!”

The next day, Nicholas slept soundly until noon, only to be awakened by a clamor.

“Say it again! What exactly is c?”

“Hippasus, you are committing blasphemy! Blaspheming the great Teacher Pythagoras!”

“The ratio of any two line segments can be expressed as the ratio of two integers. This is a universally accepted truth! How dare you question it!”

“Execute him!”

“Drown him!”