Early the next morning, Tangtang pestered Lu Jingzhi to ask him how he improved the spell contract, and Lu Jingyi refused to say it at first, he always felt that this matter was too dangerous. If there is not enough theoretical support and detailed deduction, it is very dangerous to blindly do improvement experiments. After all, before Nobel, countless chemists and even alchemists died on lax experiments. But he couldn't help but beg for it, so he had to say: "If you want to know how to improve, it's not impossible, but you have to learn one thing first, and with this skill, you can safely do all kinds of spell experiments." ”

Where would Tangtang say badly, and he was busy agreeing at the moment. Lu Jingzhi picked up a piece of parchment and wrote a sentence: between any two points, there can be one and only one straight line, and the straight line can be extended indefinitely to both ends. Tangtang read this sentence twice, raised his head, and asked, "Brother Jing, what does this mean?"

Lu Jingzhi put two small stones on the ground and said, "Look, if this ground is a piece of paper, these two small stones are two dots on the paper. Seeing that Tangtang nodded to show that he understood, he drew a line with his finger between the two small stones and said, "This is a straight line, connecting the two dots." Sugar Candy shook her head and said, "You don't draw straight." Lu Jingzhi scratched his head in embarrassment and said, "Where is it not straight? Tangtang still shook his head and said, "It's just not straight." With that, he drew his short sword from his waist and swiped it on the ground, and a straight line appeared between the two stones. Lu Jingzhi was startled, hurriedly withdrew his hand, and said with palpitations: "Sure enough, your line is straighter." Sugar Candy smiled and asked, "And then?"

At this time, Tilly walked over and saw the two of them gesturing with swords, and said strangely, "Do you usually get up so early to practice martial arts?"

Tangtang hurriedly put away the short sword and replied, "No, it was Brother Jing who taught me that I can draw a straight line between two points." ”

Tilly smiled, "I also understand this principle, and you can draw a curved line between two points." ”

Lu Jing said solemnly: "There is also below: you can use any point as the center of the circle to draw a circle of any diameter." ”

Sugar Candy didn't realize what this sentence was about for a while, and looked up and asked Tilly, "Sister Tilly, is that the case?"

Tilly was even amused when she heard this, and pulled Sugar Candy and said, "Yes, of course you can draw as big as you want to draw a circle." As he spoke, he compared his hand with his hand, "It's okay to be so big," and he enlarged his hand a little more, "It's okay to be so big." ”

Lu Jingzhi said: "Yes, if you draw a circle with a radius of 1,000 kilometers, then you will put the entire principality into it." The three of them laughed, a principality is only a few hundred kilometers in circumference, and a radius of a thousand kilometers, that is the area of several million square kilometers.

Tangtang laughed for a while and asked, "Brother Jing, is there anything else behind?"

Lu Jingzhi said: "Naturally, there is." All right angles are 90 degrees, and there is a straight line that never intersects the point outside the line. Next, he explained to Tangtang what right angles and parallel lines are.

It was only then that Tilly realized that this was a very profound science. Although they are all very simple truths, just like the elements and spells, if you really want to apply, how complex the combination is from such a simple truth.

At this moment, Lu Jingzhi also said to Tangtang: "The road is simple, and everything is very simple. But it's not easy to use it well. Like the axioms in 'Euclidean geometry' just mentioned, there are only five principles, but everything in the world is inseparable from these five principles......" Speaking of this, he suddenly got stuck, and he remembered that there are also non-Euclidean geometry, such as Riemannian geometry, Roche geometry, etc. The fifth axiom is not recognized in non-Euclidean geometry.

Tangtang nodded as if he didn't understand, and said, "Brother Jing, do these things have anything to do with the spell change contract?"

Lu Jingzhi: "The relationship is very big, this is just the foundation." You draw a circle on the paper, then you find a point from this circle, and you draw a line, which must pass through this point, and can only intersect this circle at this point, and this line is the tangent of the circle. ”

Sugar Candy used a short sword to draw a circle on the ground, which was more standard than the compass, and it was exactly drawn on the straight line just now. Lu Jingzhi clapped his hands and said, "That's it." As he spoke, he asked Tangtang to draw another five straight lines, forming a regular hexagon with the line just now. The straight lines of the sugar candy are evenly drawn and the angles are exactly the same, as if they were drawn with a ruler. Lu Jingzhi is used to seeing it, and he has long been accustomed to it. This hand-eye control ability is a necessary quality of the Golden Arrow, if you can't do it with the same heart, hand and eye are the same, it is impossible to play a role in the battle to move the whole body. But Tilly thought it was quite amazing, she knew that this was Tangtang's talent, and she would never be able to do it if she changed to someone else.

It wasn't until Lu Jingzhi talked about bringing out calculus through the tangent of a circle, that Tangtang's comprehension ability completely collapsed. She couldn't figure out what it had to do with the spell. Lu Jingzhi spoke with a dry mouth, and Tang Tang couldn't understand one percent of it.

"After all, what are you studying?" Tilly looked at Lu Jingzhi, who was blushing, and Li Tangtang, who was confused, what are these two people struggling with?

"It's Brother Jing who is teaching me how to draw. Sugar Candy said a little frustratedly, "But I'm too stupid to learn." ”

Lu Jingzhi hurriedly shook his hand and said, "No, no, it's not that you're stupid, in fact, you've learned a lot of things beyond your age." Your brother may not be able to do these things. ”

Tangtang was silent when she heard this, and she was worried about Li Boyang again. In fact, when a girl reaches her age, it is the time when she will suffer from everything, and she may be happy about everything, or she may be depressed because of a word.

Tilly looked at the five axioms and the basis of calculus written by Lu Jingzhi, thought about it again and again, and asked, "What kind of science is this?"

Lu Jingzhi was not happy to coax Tangtang no matter how much he coaxed him, so he had to put it down for the time being, turned back to Tilly and said, "This is mathematics." ”

In fact, everything is inseparable from mathematics. Only mathematics is the most ingenious of the sciences. Whether it's a hand-drawn figure by Sugar Candy or a bell cast by Tilly, they can be reproduced with mathematical models. But mathematics is very delicate and fragile, and a self-consistent mathematical model can become very different if it is affected by any external influence. Lu Jingzhi was influenced by his father since he was a child, and he liked to build mathematical models for everything, and felt that it was natural to be able to deduce these spells in his mind, but in the eyes of Sugar Candy and Tilly, this was almost a skill close to a miracle. However, mathematical knowledge is not something that can be achieved overnight, he only learned some basic mathematical knowledge after several years of hearing and seeing by his father, where can Tangtang learn it all at once? It's just that Lu Jingzhi himself didn't understand the key to this, and he couldn't teach Tangtang in one go, knowing everything, saying everything, and Tangtang himself didn't understand why Brother Jing knew so many things, but he didn't understand at all. When she followed Li Boyang out of the house, she didn't even go to elementary school, and she had to learn the courses of junior high school and even college all of a sudden.

Fortunately, Tangtang didn't drill the horns of the bull, and knew that he couldn't learn it, so he put it aside first, pulling Tilly to talk non-stop, leaving Lu Jingzhi to think about the spell on the side. He was almost certain that the spell was a kind of magic array, something like an alchemical formula or a formation. Listening to what Tangtang told herself, it seems that there are various elements in this world, and the elements can be affected by the formation drawn on the paper, automatically filtered and arranged, and can also be mixed to create various effects. This was almost unheard of in the world before. On the other hand, the seven bells on Tilly's body seem to have nothing to do with these elements, but shake different sounds through different lines, and then act on the undead who can hear the sound through the sound. It seems that there is more than one way to use these spells.

"Brother Jing, what are you thinking?" Tangtang was talking happily on the side, and when he saw Lu Jingzhi frowning, he thought he was unhappy, so he came over to ask him.

"You say, what would happen if we carved the spell deed on the stone?" Lu Jingzhi asked thoughtlessly.

"That's the enchanted stone. Tilly replied that she had done this kind of thing in all the years she had followed her teacher, "I used to form a border with spell stones on the edge of the ancient forest to prevent the undead from coming to this world through the gates of the underworld. ”

"Oh......" Lu Jingzhi responded, so even a stone can be affected by the elements, so if you carve a mixed spell on the stone and throw it out, it should be able to explode like a grenade. He deduced several figures in his mind, which could allow various elements to temporarily accumulate without mixing, to accelerate the convergence of mixed elements, to limit the expansion of elements and accumulate pressure, and then to merge them one by one to form a large magic array. When these formations were fused, Lu Jingzhi couldn't help but smile, and when he looked up, it was almost noon. It turned out that he was here just speculating, and almost 3 hours had passed. Tilly had already walked away impatiently, she was the commander of the principality's army, and she had to worry about marching and camping, so naturally she couldn't waste time with them. Only Sugar Candy has been with him on the side.

Tangtang also knew that Lu Jingzhi had a problem sinking into his thoughts, and if he was thinking very complicated, he was often most afraid of being disturbed. When encountering such a situation, she often sent Sijiu and Yinxin away from the distance, and also ordered that no one should quarrel, and that she should just sit quietly and accompany her. At this time, seeing Lu Jingzhi smiling, knowing that he had figured out a key matter, he also became happy.

How exactly does Lu Jingzhi want to realize the enchantment? I want to know what happens next, and let's see the next decomposition.