A tangent line only intersects a curve at one point.
It takes two points to determine a straight line.
However, there is only one tangent line through a point.
These three sentences are completely fine when viewed separately, but when combined together, Ella feels logically confused. Countless straight lines can be drawn through a point, but the tangent line passing through this point is unique. Is this a problem?
After some thinking, Ella figured out the reason: each individual property in infinity is different, and there is only one with the property of 'tangent'.
In other words, tangent is the only one among infinity.
But the problem is that without two points, people cannot make a definite straight line. And if we use the elimination method to eliminate all the infinite possibilities and work backwards to find the only one among them, 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 make it?"
This reminded Ella of the entire natural world - people can understand the properties of water, air, and soil, but people cannot create water, air, or soil.
This feeling of powerlessness made Ella begin to feel that the teachings of the Abrahamic Church were correct - God arranges everything in the world, and humans can only watch and cannot imitate.
"No, if you admit this, you will never be able to learn Pythagorean magic!"
Ella patted her cheek. Although she is now in a spiritual state, the action itself can cheer her up.
"Ella, don't be afraid of infinity!" She encouraged herself. "Since two points can determine a straight line, then just find two points!"
If you really find two points on a straight line, the line you make will be a secant line instead of a tangent line. But Ella knows that as the two points continue to approach, the secant line will continue to approach the tangent line.
With her previous experience in finding the area of a curve, Ella quickly thought of a similar trick - making the distance between the two points infinitely close but not equal to zero. This number must be small enough, otherwise the line drawn will deviate from the tangent line; 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 expressed these two points like this: (x, y), (x+dx, y+dy), where dx and dy represent numbers that are infinitely close to zero but not equal to zero. As long as the slope of the tangent line is calculated through these two points, the tangent line can be found.
After putting these numbers into the curve y=x2, the formula is very simple, unlike the infinite series that is involved in finding the area of the curve that adds up to infinity.
Ella tried changing the function to y=x3, y=x4, y=x5, but the difficulty of calculation did not change much.
"This is too simple!"
Ella shouted happily. She wanted to share this discovery with others and wanted to celebrate this discovery by slaughtering fifty cows! .
However, no one paid any attention to Ella.
Members of the Ancient Abrahamic Church have re-translated "The Technique of Chariots to the Sky" from memory. For several days, like Jochebed, they buried their heads deeply between their knees and chanted protective incantations over and over again, trying to understand the miracle of God.
This scene seemed familiar to Ella - when she was in Constantiniya, whenever she tried to explain her new discoveries about celestial bodies to people, they would always lower their heads in panic and use vague words to look towards the gods in fear. prayer.
Whenever this happens, Ella will feel that she is an alien, an ugly duckling among a group of white swans.
She lowered her head in disinterest. 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 with numbers. The clown on the stage can still make everyone happy with his tricks, but this trick can't even do that.
Someone came to her. But she had no intention of looking up. No matter how many people gathered around her, all she felt was boundless loneliness, just like every time she observed the stars.
A drop of water - or something like water dripped on the empty manuscript paper. The man who came to her looked carefully at what was on her manuscript paper and said, "It's amazing."
"Do you understand? It's interesting, right?"
Ella suddenly became excited. But when she raised her head, she saw a terrifying sight - the face of the spirit in front of her was covered with red corpse spots, diatoms were stuck to her hair, her nose and nails were filled with sand, and her skin was It was shriveled as if it had been soaked in water for too long.
Ella screamed in fright and hurriedly moved back a few steps, but the spirit body pursued her relentlessly. He tilted his head, staring at the manuscript paper in Ella's hand with extremely empty eyes, repeating two words over and over in his mouth: "Incomprehensible, amazing; incomprehensible, amazing; incomprehensible, amazing Amazing..."
"You...who are you?"
The spirit moved its gaze from the manuscript paper to Ella mechanically. The crazy re-reading stopped, he smiled strangely, and suddenly raised a hand to grab Ella's face.
Ella screamed again in fear. Through the transparent spirit body, she saw that the members of the Ancient Abraham Church still kept their heads buried in their knees, and were completely indifferent to her screams twice.
Ella smiled miserably: "Ah... So that's it... I'm completely... a superfluous person."
The spirit caught her. In an instant, the tragic memories from that spirit body poured into Ella's heart——
"Sibsos, look what you have proven?"
"Sibsos, you unleashed the demon!"
"You shouldn't have entered this realm! Sibersos!"
——Transparent sea water, illusory sunshine.
There were also ugly fish swimming in front of her eyes.
The biting sea water stimulated every nerve in her. She felt suffocated, but could not struggle because her hands and feet were tied to death by ropes. She was terrified, but couldn't scream because sea water had filled her esophagus and stomach.
A group of mathematicians on the ship looked at her without mercy. The man at the head was Pythagoras. His voice penetrated through the sea water and penetrated every bone in Ella's body: "Sink to the bottom of the sea... along with your pathetic proof."
In 500 BC, Sibersus discovered irrational numbers. That was the first time humans understood infinity mathematically.
He was then thrown into the sea by the Pythagoreans.
She could do nothing but let her body fall into the abyss of the sea, watching helplessly as the sky got further and further away from her.
The ship full of mathematicians continued to float on the sea, like a carefree fish.
…
"Come back quickly, that spirit body has been blown up by your memory. I'm not telling you, the amount of your memories... is really unbearable."
"But thanks to this, I know what you're doing."
Gottfried's voice penetrated the water and dragged Ella.
"This is a great work that has never been done before. Come, I will help you complete it."
Barcelona's Restoration Diary
