Three carriages lined up in a row and drove quietly in the countryside of the Duke of Valua.

More than 20 members of the ancient Abraham church sat in these three carriages. The "Carriage of the Chariot" was also cut into three pieces and held by people on the three carriages. On the one hand, this is to accelerate the deciphering of the cipher text, and on the other hand, it is to prevent anyone from wanting to monopolize the "Carriage of the Chariot".

It has been a full month since Ella and his men were teleported to the Ile de France by magic. The deciphering of the "Type of Chariots" is coming to an end with the cooperation of more than twenty members of the ancient Abraham church.

But in space, they were still circling around the Ile de France - although they were not caught by the Count of the Ile de France, they did not approach Stade at all. If they drew the route they had taken on the map, they would find that they were conducting a carpet search of the Ile de France than escaping from the Ile de France.

No one stood up to explain this strange route. Because the planner of this strange route, Ella Cornelius Scipio, was working on math problems from beginning to end.

In one month, Ella's mathematical research made great progress.

Using the inspiration obtained by the spider's dream, Ella drew two horizontal and vertical numbers on white paper at ninety-degree angles.

Ella named the system composed of these two axes as coordinate axes.

In this way, any point on the white paper can be represented by the coordinates of a number. Any geometric figure is composed of infinite points. In other words, using this coordinate axis, any geometric figure can be converted into numbers.

——Geometry and number are unified on this basis.

Ella felt that she had taken a big step towards the Pythagoras school's idea of ​​"everything is counted", and she couldn't help but want to tell Gottfried about this discovery several times.

However, Gottfried, who is working to crack the "Trolleys of the Sky", has no intention of listening to Ella talking nonstop. Ella ran over several times, but Gottfried was perfunctory.

Later, as soon as Ella appeared in front of Gottfried's carriage, without even having to speak out, the people next to him would drive her away like a fly.

Habiba seemed to have seen the opportunity to make money, and smiled and said to Ella, "Miss, my apprentice has a bad temper, but I just listen to me. If you really want to learn mathematics, give me five Nomismas, and I guarantee that he will teach you honestly. If he doesn't want to, I can tie him up and throw him away to your room."

But even Habiba added in the end: "However, we have to wait until we decipher the "Trails of Chariots"."

According to these members of the ancient Abraham church, the "Tacle of Chariots" records the method of measuring infinite gods. By learning it, you can understand the nature of the Supreme God and gain power far beyond any kind of protection.

In order to get rid of the dilemma of being chased by the apostles as soon as possible, they kept decorating the "Tacle Climbing the Sky" day and night, each person only slept for three hours a day on average. After this month, they had reached their limit and had no time to care about math problems.

Ella could only retract back to the corner of the carriage in disappointment, and continued to write and draw on the paper alone. In revenge, when someone asked her why she took this route, she always said perfunctorily: "Wait until I finish this question."

During this time, she expressed all the common geometric figures in a function based on the axis. Then, the problem returned to the parabola.

Parabola is a curve. Experience tells Ella that whenever a problem is related to a curve, the difficulty will suddenly become greater.

Through the coordinate axes, Ella can already describe various curves with numbers. In order to give herself some confidence, she first chose the simplest parabola: y=x² for research.

She made a straight line y=1, which intersected with the parabola at a point a. In this way, the three lines of the parabola, the straight line, and the x-axis form an irregular geometric figure.

Ella wanted to calculate the area of ​​this irregular figure.

She found points on the parabola and made two lines perpendicular to the x-axis and y-axis, thereby dividing the irregular figure into rectangles. The area of ​​these rectangles is obviously greater than the area of ​​the irregular figure. However, the thinner the rectangles are divided, the closer their area will be to the irregular figure.

Ella assumes that N rectangles are divided between the straight line from the origin of the coordinate axis to y=1, then the width of each rectangle is 1/N. And because the function of the parabola is y=x², then the height of the first rectangle is (1/N)², and the height of the second rectangle is (2/N)²…

Then, the sum of the areas of all rectangles is:

S=1/Nx(1/N)²+1/Nx(2/N)²+…+1/Nx(N/N)²

This is an infinite series. However, Gottfried once taught Ella's sum of squares formula for the infinite polynomial. After using this formula to simplify this infinite series, she got an extremely simple formula:

S=1/3 1/(2N) 1/(6N²)

The larger N, the closer the sum of the area of ​​the rectangle is to that irregular figure. Then when N is infinitely large, the sum of the areas of the rectangle S will be equal to the area of ​​the irregular figure. At this time, 1/(2N) and 1/(6N²) are infinitely small, and can be completely abandoned.

So the area of ​​this irregular figure becomes obvious: S=1/3.

——Infinitely large, infinitely small

Ella whispered the two concepts that had just appeared. The concept of infinite appeared in mathematical operations, which made her feel a little uncomfortable.

She shook her head, threw this discomfort behind her, and then changed the function from y=x² to y=x³

Although it was only a slight change, the difficulty of requiring area was immediately increased several times. This time, Ella wrote two pages of paper, but she failed to simplify the formula as before.

"Why does it always appear when curves are involved!"

Ella threw down her pen and wailed with her head.

Infinity, this is an abyss that all mathematicians cannot cross.

Both parabola and circle are just the simplest curves, just a small branch that pops out from the infinite abyss. Ella grabbed the branch. But when she continued to look down, she saw a more terrifying abyss - using the axis and function, she found many complex curves that Archimedes could not describe at all.

She found them, but could not control them at all. This seemed to be a warning from the gods: Man, do what you should do!

Infinite, this is a forbidden zone that humans must never enter.

"The magic of the Pythagoras School is too difficult to learn!"

Ella shouted again.

"Speak quietly!"
Chapter completed!