A bonfire was lit in the yard. The nun was holding a book and sitting on a stone outside the door, telling stories to the children surrounding her.
Ella watched them silently from the second floor until the nun felt it was too late and asked the children to go back to their rooms to rest. During this period, every movement of the children revealed their love for the nun.
If this is not the church of the Abrahamic Orthodox Church, but the temple of the Seven Hills Empire, will the priests take in the travelers? Will they adopt abandoned children? Will these children love it so much?
——This kind of thing should still depend on the individual, right?
Ella shook her head to get rid of the ridiculous idea that just appeared in her mind, and then took out a stack of paper and placed it on the table. There were some unsolved geometric problems on it.
One of them is a parabola, and a line cuts through it diagonally, forming an arc together with the parabola. Gottfried's task for Ella was to calculate the area of this arc.
Ella thought about it, took the straight edge of the arc as the base, and chose a point on the parabola, and connected them together to form a large triangle. Then, using the other two sides of the large triangle as the base, they each chose a parabola.
A point on the top connects two small triangles.
Ella stared at these three triangles. According to Gottfried's method of calculating the area of a circle, if these triangles continue to be drawn, the sum of their areas will get closer and closer to the area of this arc.
However, the triangles drawn in this way will have various sizes and irregularities depending on the selected points. If you want to calculate the area sum, you must formulate a unified drawing rule.
Ella sighed, tore up the paper and drew a new one. This time, she moved the straight line parallel until it cut the parabola at a point. Ella drew the first big picture with this point as the vertex.
Triangle. Then she used the same method to draw two triangles at the next level.
In this way, the problem immediately became clear. After a period of geometric proof, Ella found that the sum of the areas of the two small triangles was one-quarter of the large triangle. And the area of the two small triangles at each level was
and are both one-quarter of the previous large triangle.
Ella tentatively assumes that the area of the first large triangle is a, and the area of the bow is s. Then, the area of the bow is like this:
s=aa/4a/16a/64…
This is a calculation that expands infinitely and seems to yield absolutely no results.
——Infinite again.
Ella put down her pen and let out a long sigh. The only person who can calculate infinite numbers is probably the God of Mathematics.
However, the side length of the square with an area of 1 warned Ella: she cannot give up just like this.
In Gottfried's words, since it is a finite line segment, it cannot be infinite. Similarly, this bow shape is obviously a finite area. From a geometric point of view, it is there, unlike other
There is nothing special about the graphics.
Ella patted her head and stared at the finite figure again and the infinitely expanding equation listed below.
Suddenly, she had an idea, picked up her pen and multiplied both sides of the equation by 4. According to the law of equation, the equation still holds at this time. But this time, the equation became as follows:
4s=4aaa/4a/16a/64…
Ella noticed that the numbers on the right side of the equation were exactly the same as the previous equation starting from the second term. With trembling hands, she simplified the equation to this: 4s=4as
The infinitely extended equation suddenly becomes a finite, simple equation. Even a novice child can figure out the result at a glance:
s=4a/3. The area of the bow is 4/3 of the area of the first large triangle
Just multiply it by 4, and infinite becomes finite?
Ella felt a little dizzy and couldn't figure out why this happened. As Gottfried said, solving geometric problems depends more on personal skills and a moment of inspiration than on just one.
Numbers that can be obtained step by step by writing out calculation formulas are completely different.
Moreover, the question is not actually solved - what is the area of this large triangle?
Not to mention the area of this big triangle, in fact, Ella doesn't even know how to describe this parabola. Knowing the radius can determine a unique circle, knowing the length and width can determine a unique rectangle, and knowing the three sides can determine a unique rectangle.
triangle. What parameters are needed to determine a unique parabola?
"Is everything numbered...?"
Ella once again looked out the window. The world is so vast and the Milky Way is so bright. If it is correct to say that "everything is number", then everything in the world, as well as the process and method of its movement, are
Can it be expressed using numbers and formulas?
So is there an ultimate formula that can deduce everything in the world?
Ella shook her head again, wondering why she had so many ridiculous thoughts today. She returned her attention to the paper and looked at the graph on it. Not to mention that everything was numbered, even this simple parabola
, she couldn't even convert it into numbers.
"I thought Pythagorean magic would be easier for me..."
Ella felt her head hurt, so she put away the paper and hurriedly lay down on the bed.
A spider hung from the roof in front of her eyes, swaying up and down and left and right.
Ella put out the light, but for some reason the spider lingered in her mind.
She had a dream. In the dream, the corner of the wall and the ground formed three mutually perpendicular straight lines, which were densely covered with numbers from small to large. The spiders became dots that were constantly moving between them, drawing lines all at once.
Draw a square, and then draw a circle, and then it becomes a parabola...
Early the next morning, Ella found Habiba huddled in the corner angrily, apparently because something went wrong during last night's "teaching". And Gregory criticized him righteously:
"I thought that your ancient Abrahamic Church, which has been passed down for more than a thousand years, must have some high-level opinions, but I didn't expect that what you said was such vulgar words! Your Kabbalah theory represents God as infinite, but you self-righteously created ten
A mapping and twenty-two paths, it is said that this is the whole process of infinity transforming into us. But is this process division or subtraction? Whether it is division or subtraction, since it is infinite, after thirty-two steps, it is still infinite.
?Do you want to say that you, me, and him are all infinite? You also say that through these twenty-two paths, people can lead to infinity. Is this process addition or multiplication? Whether it is addition or multiplication
, after twenty-two steps, isn’t the finite still finite? The infinite and the finite are like separated by an abyss! It is simply unreasonable to try to understand the infinite through finite steps!”
Habiba couldn't answer a word and could only glare at Gottfried from time to time to vent his dissatisfaction.
Gottfried, trembling from the side, interrupted Gregory and said, "Didn't you say you wanted to learn the magic of the ancient Abrahamic Church..."
"Shut up! How dare you talk here! I want to learn magic, but I don't want to be tempted by the devil! What I believe in is always the only true God! If I can really understand the nature of the infinite God, just let me learn magic. But you
Master's theory makes me feel that your magic comes entirely from demons! You should seriously consider whether you have been led astray by your master!"
"The Techniques of Ascending a Chariot to the Sky..." Habiba said angrily, "Maybe the "Techniques of Ascending a Chariot to the Sky" will have the answers to all of this."
Gregory took a few deep breaths, suppressed his anger in his heart, and then said: "Is this "The Technique of Chariots Ascending to the Sky"? Okay, okay, let me see what is written in it."
Habiba shrank her head: "But there is a high probability that we won't be able to get in with our clothes now, so why not forget it today..."
"What about clothes? I'm ready!"
——"Yes, someone just sent the clothes and asked me to hand them over."
The priest of the church suddenly appeared and handed some clothes to Gregory.
"There are two roads to the auction venue. There are many carriages on the main road and it is easy to get jammed. It will be faster if we take the small road."
The priest gestured in the air to show Gregory the way, and then went about his own business. When he was about to reach the corner, he turned around and saluted Gregory, but neither Ella nor the others noticed.
"It was the same in the mountains before, and it's the same now. Whether it's money or clothes, someone will deliver them to you overnight. Could it be that you are actually a big businessman, and you have branches in these places? But why are your clothes...
…?” Ella asked with some confusion.
"For businessmen, dressing up on the road has no use except increasing the danger." Gregory panicked following Ella's words. "Miss, do you want to go with me? I'm sure
Prepare your clothes."
Ella thought for a while: "Well, I don't know what the "Chariot Transformation Technique" is for, but the auction seems to be quite interesting. I just don't have any ideas for geometry problems right now, so I might as well go and take a look.
"
So Ella put on the clothes prepared by Gregory. It was silk from the East. It was very soft and thin, and it looked expensive at first glance. For nobles and wealthy businessmen, such expensive clothes were expensive.
Put on and take off carefully to avoid wrinkles.
When Ella took it, she crumpled it into a ball casually.
This made Gregory a little confused. He thought Ella was the eldest lady, but this behavior seemed to be completely ignorant of the value of the clothes. It was simply something that farmers who bury their faces in the fields all day would do.
.
He didn't know that for Ella, this was just slightly better casual clothes. The purple robe that Ella burned to comfort Amy was much more expensive than this dress.
However, Gregory didn't pay too much attention to this. Clothes were just clothes, so wear them however you like.
However, when Habiba and Gottfried reached out to take their clothes, Gregory couldn't help but pull their hands away because they were really too dirty.