Meet the principal

On the third floor of the teaching tower, in Classroom 301, Reiner was sitting on a chair. He had several drawings at hand. The sunlight hit the side of his face through the window, showing a certain concentration.

Claire was sitting a little further away. She didn’t know why Reiner wanted to find her here. Although she heard that it was to assist in experiments, this place was just an ordinary classroom. It was used to teach courses such as the history of magic. Where? Is there room for experimentation?

And Reiner has just won the Hohenheim Gold Cup, so is there any new discovery?

With many questions in mind, Claire saw a girl at the door of the classroom timidly looking inside, afraid to step into the classroom.

"Dana?"

Claire recognized this student as Dana Kristen, whom Reiner mentioned yesterday.

"Uh, Teacher Claire."

When Dana's name was called, she walked in cautiously. She looked at Claire and then at Reiner before speaking in a soft voice.

"I just came here to take a look. If anything goes wrong, I will leave immediately."

"It doesn't matter."

Reiner was not surprised because he knew that Dana would definitely come.

"Now that everyone is here, let's start today's agenda."

Clapping his hands, he came to the podium and faced the two people sitting down. It seemed that Reiner was the teacher.

"Wait, you haven't said what you're going to do today?"

Claire raised her hand and asked, a bit complaining, because it seemed like Dana knew something about the situation.

"Well, I want to improve the spell model a little bit. To be precise, the way the spell model is interpreted."

Reiner said lightly, then turned around and started drawing something on the blackboard with chalk.

But his words stunned Claire and Dana.

Improved spell model? ? ?

The spell models currently used have been determined through countless practices and have reached perfection, but Reiner casually said that he wanted to improve the spell model?

If it weren't for the fact that he had won the Hohenheim Gold Cup before, Claire would have felt that Reiner was playing a trick on her.

Dana was silent as she watched Reiner draw a familiar pattern on the blackboard, which was the spell model of illumination.

The zero-ring spell is constructed based on the plane. All the spell nodes are located on a plane, which is quite simple.

The five magic nodes and the seven magic channels connected to them form the basic model of this spell. The magic channels have three curves and four straight lines, which seem to have no rules.

Seeing this spell model, Dana bit her lower lip and pinched the corners of her clothes with both hands, as if she was recalling bad memories.

This was the exact spell she had failed to cast yesterday.

"This spell model is a model of illumination. The deviation between the relative position of the node and the magic channel will cause the spell to fail. Of course, insufficient magic will also cause similar failures."

Reiner checked Dana's magic power test document and found that her magic power was not insufficient, but rather higher than ordinary people. Therefore, the main reason for the failure of spell casting should be her mistake in constructing the spell model.

"Dana-san, I would like to ask you how you construct the spell model?"

Hearing Reiner's question, Dana hesitated for a while before speaking.

"First construct the Loire Cartesian coordinate system, calculate the coordinates of each node, and then establish the functional equation of the magic channel..."

The Loire rectangular coordinate system she was talking about was proposed two hundred years ago by the late Lord Andre Loire, the master of the law system. It is a mathematical tool used to describe magic models. It is similar to that on the earth. On the plane , this coordinate system consists of two mutually perpendicular coordinate axes, so it is called a rectangular coordinate system.

On a plane, such a coordinate system can clearly mark the location of each magic node, which is accurate and practical.

By changing the position of the coordinate origin, it can also adapt to different situations.

"is that so?"

After listening to Dana's words, Reiner established coordinates on the spell model and marked the locations of each spell node.

Then, he began to write the functional equation of the magic channel. This was also a concept proposed by His Excellency Andre Loire. It is a mathematical expression that describes the correlation between one variable and another variable. Previously, Reiner and Anto What Wan uses to set up the magic signature is a function equation.

However, compared to the magic node, the function equation of the lighting magic channel is obviously much more complicated. Due to the existence of curves, it is very cumbersome to express and requires a lot of calculations.

Dana looked embarrassed when she saw the familiar formula, but she still nodded.

Claire still didn't know why, but she had previous experiences. She suppressed the doubts in her heart, did not speak rashly to avoid being slapped in the face by Reiner, and listened intently to Reiner's lecture.

"Dana, I think a large part of the reason for your failure in casting spells is that there was a problem when you constructed the spell model. I have a test paper here. I hope you will spend half an hour to do it carefully."

Reiner pulled out a handwritten test paper and handed it to Dana.

The student took the test paper and soon turned pale.

Because it’s all math questions.

From basic calculations to complex solutions to functional equations, there are ten questions in this test paper, which is roughly equivalent to the level of high school students on earth.

Dana glanced at Reiner, her eyes seemed to be filled with resentment.

Despite this, she still picked up the quill on the table and started working on the questions.

"So now we just wait for her to finish?"

Claire asked quietly, and Reiner shrugged, then handed Claire a piece of paper.

"Why don't you try it too?"

It has the same title as Dana.

"Hmph, I won't be fooled."

The same trick will never work twice, so Claire is naturally not afraid of Reiner's provocation.

However, her curiosity still prompted her to look at the questions on the test paper. When she saw the first question, Claire's face darkened.

In triangle ABC, it is known that AB=2, AC=3, angle A=60 degrees, find the length of BC and the value of sin2C.

"..."

"It's okay, there's no shame in not being able to do it."

Reiner smiled and said that this kind of question is quite difficult for students like Dana to be honest, but the calculation of geometric relationships on the plane is also necessary for mages to build spell models.

"Humph, don't underestimate me!"

Claire glanced at Reiner, and then picked up the quill and started drafting, but it was obvious that she could complete the questions much faster than Dana.

Half an hour passed quickly, and both of them handed in their test papers.

Although Claire made many mistakes and some questions that she couldn't write, she still met the standard.

As for Dana, none of the questions had a correct answer, which made her a little frustrated.

"I'm really not suitable to be a mage."

Dana muttered.

"No, Dana-san, you just lack some basic training and more appropriate methods."

Reiner's words made the originally dejected student slowly raise his head.