The tangent only intersects the curve at one point.

Only two points can determine a straight line.

However, through one point, there is only one tangent.

These three sentences are completely free of problems when viewed separately, but when they are connected together, Ella feels logically confusing. You can make countless straight lines through one point, but the tangent line passing through this point is unique. Is there any problem?

After some thought, Ella figured out the reason: every individual in the infinite has different properties, and only one with the property of "tangent".

In other words, the tangent is the only one in the infinite.

But the problem is that without two points, people cannot make a definite straight line. If we use the method of elimination to eliminate all the infinite possibilities and find the only one in reverse, it sounds like only gods can do it.

"I know the tangent is there, and I can understand all its properties, but I can't find its function expression?"

This reminds Ella of this whole world of nature - people can understand the properties of water, the properties of air, and the properties of soil, but people cannot create water, air, and soil.

This sense of powerlessness made Ella feel that the teachings of the Abraham church were correct - God arranged everything in the world, and people could only watch and could not imitate.

"No, if you admit this, you will definitely not be able to learn the magic of the Pythagoras school!"

Ella patted her cheek. Although she was in a spirit state now, this action itself could cheer her up a little.

"Aira, don't be afraid of Infinity!" She encouraged herself. "Since two points can only determine a straight line, just find two points!"

If you really find two points on a straight line, the line you make is a separator instead of a tangent. But Ella knew that as these two points keep getting closer, the separator will be constantly approaching the tangent.

With the previous experience of finding the area of ​​a curve, Ella quickly thought of a similar trick - to make the distance between these two points infinitely close and not equal to zero. This number must be small enough, otherwise the line made will have a deviation from the tangent; at the same time, it must not be equal to zero, otherwise there will be only one point left and the straight line cannot be determined.

Ella expresses these two points in this way: (x,y), (x dx,y dy), where dx and dy represent the number that infinitely close to zero but not equal to zero. As long as the slope of the tangent is calculated through these two points, this tangent can be found.

After bringing these numbers into the curve y=x2, the formula is very simple, and it is completely different from the infinite series that involves adding to infinite when calculating the area of ​​the curve.

Ella tried to change the function to y=x³, y=x⁴, y=x⁵, and the difficulty of calculation did not change much.

"This is also too simple!"

Ella shouted happily. She wanted to share this discovery with others, and wanted to slaughter fifty cows to celebrate this discovery!

However, no one paid attention to Ella.

Members of the ancient Abraham church had re-translated the "Tacle of the Chariot" based on memory. For several days, like Jogipai, they buried their heads deep between their knees, chanting protective spells over and over again, trying to understand God's miracle.

This scene is familiar. Whenever she tries to explain her new discoveries of celestial bodies to people, those people will always lower their heads in panic and pray to the gods in a vague sentences.

Whenever this happened, Ella felt that she was an alien, an ugly duckling among a group of white swans.

She lowered her head in delight. Looking at the manuscript in front of her, she suddenly felt a little doubtful - do these things have any value? This seems to be just a trick of playing with numbers. The clown on the stage can still make everyone happy with her own tricks, but this trick cannot even do this.

Someone came to her. But she had no intention of looking up. No matter how many people gathered around her, what she felt was endless loneliness, just like every time she observed the starry sky.

A drop of water—or something like water dripped on the empty manuscript paper. The man who came to her looked carefully at the things on her manuscript paper and said, "It's amazing."

"Did you understand? It's very interesting, right?"

Ella suddenly became excited. But when she raised her head, she saw a terrifying scene - the spiritual body in front of her was covered with red corpse spots, diatoms were stuck to her hair, and her fingernails were covered with mud and sand. Her skin was wrinkled as if it had been soaked in water for too long.

Ella screamed in fear and hurriedly moved back a few steps, but the spirit body chased after him. He tilted his head and stared at the manuscript paper on Ella's hand with an extremely empty look. Two words were repeated over and over again in his mouth: "It's amazing that people can't understand; it's amazing that people can't understand; it's amazing that people can't understand..."

"You...who are you?"

The spirit moved his gaze from the manuscript paper to Ella mechanically. The crazy replies stopped. He smiled strangely, suddenly raised a hand and grabbed Ella's face.

Ella was so scared that she screamed again. Through the transparent spirit, she saw that the members of the ancient Abraham church were still burying their heads in their knees, and were completely indifferent to her screams twice.

Ella smiled miserably: "Ah...so that's it...I'm completely...a redundant person."

The spirit grabbed her. In an instant, the tragic memories from that spirit poured into Ella's heart—

"Sibersus, see what it proves?"

"Sibersus, you let the demon go!"

"You shouldn't have stepped into this field! Sibersos!"

——Transparent sea water, illusory sunshine.

There were also ugly fish swimming by her eyes.

The bone-breathing sea water stimulated every nerve of her. She felt suffocated but could not struggle because her hands and feet were tied to death by ropes. She felt frightened but could not shout because the sea water had filled her esophagus and stomach.

A group of mathematicians looked at her on the boat without any mercy. The man in charge was Pythagoras. His voice penetrated through the sea water and penetrated every bone in Ella's body: "Sink to the bottom of the sea... together with your sad proof."

In five hundred BC, Sibersus discovered irrational numbers. That was the first time that humans had a mathematical understanding of infinite numbers.

Then he was thrown into the sea by members of the Pythagoras school.

She could not do anything, and could only let her body fall into the abyss of the sea, watching the sky get farther and farther away from her.

The ship full of mathematicians continued to float on the sea, like a carefree fish.

...

"Come back soon, that spirit has been blown away by your memory. It's not me that the amount of your memory... is really unbearable."

"But thanks to this, I know what you're doing."

Gottfried's voice penetrated the sea and dragged Ella.
Chapter completed!