On the third floor of the teaching tower, in classroom 301, Reiner was sitting in a chair, he had several drawings in his hand, and the sunlight through the window hit the side of his face, showing a bit of concentration.

Claire sat a little farther away, she didn't know why Reiner had asked her to come here, although I heard that it was to assist in experiments, but this was just an ordinary classroom, which was used to teach courses such as the history of magic on weekdays, where was there room for experiments?

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

With many questions, Claire saw the door of the classroom, and a girl looked inside timidly, and did not dare to step into the classroom.

"Dana?"

Claire recognized the student as none other than Dana, whom Reiner mentioned yesterday. Christine.

"Uh, Mr. Claire."

Dana was called by her name, and then she cautiously walked in, she looked at Claire and then at Reiner before speaking in a soft voice.

"I'm just coming over and looking, and if there's anything wrong, I'm going to leave immediately."

"It's okay."

Reiner wasn't surprised, because he knew Dana would definitely come over.

"Now that we're all together, let's start today's agenda."

Clapping his hands, he came to the podium, facing the two people sitting down, as if Reiner was the teacher.

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

Claire asked, with a hint of grumbling, as it seemed that Dana knew something.

"Well, I'd like to revamp the spell model a bit, or more precisely, the way the spell model is interpreted."

Reiner said lightly, then turned around and began to draw something on the board with chalk.

But his words made Claire and Dana stunned.

Improved Spell Model???

The spell models used now have been determined after countless practices and have reached perfection, and Reiner casually said that he wanted to improve the spell models?

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 herself.

Dana was silent as she watched as Reiner drew a familiar pattern on the blackboard, a model of a light spell.

Zero Ring spells are built on a plane, and all spell nodes are located on a plane, which is fairly simple.

The five spell nodes are connected to each other and are connected to seven mana channels that form the base model for this spell, and the mana channels have three curves and four straight lines, which seem to have no pattern to follow.

Seeing this spell model, Dana bit her lower lip lightly, and her hands clenched the corners of her clothes, as if she remembered bad memories.

This is exactly the spell she cast unsuccessfully yesterday.

"This spell model is a model of illumination, and deviations from the relative position of the nodes and the mana channel will cause the cast to fail, and of course, a lack of mana will produce a similar failure."

Reiner had reviewed Dana's mana test documents, and instead of being deficient, her mana was a little higher than normal, so the main reason for the failure was her mistake in building the spell model.

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

Hearing Reiner's question, Dana hesitated for a moment 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......"

What she refers to as the Cartesian coordinate system of the Loire was developed by the late master of the Law System Andrew. A mathematical tool proposed by Lord Loire two hundred years ago to describe the model of spells, similar to that on Earth, this coordinate system is made up of two coordinate axes perpendicular to each other, hence the name Cartesian coordinate system.

On the plane, such a coordinate system can clearly mark the position of each magic node, which is accurate and practical, and can also adapt to different situations by changing the position of the coordinate origin.

"Is that so?"

Reiner listened to Dana's words and set up coordinates on the spell model, marking the locations of each spell node.

He then began to write the equations of the functions of the magic channel, which was also written by Ander. The concept proposed by Lord Loire is a mathematical expression that describes the correlation between one variable and another, and it was a functional equation that Reiner and Antoine had previously used to set up their magic signatures.

However, the equations for the Illumination Mana Channel are obviously much more complex than the Mana Node, and due to the curves, they are cumbersome to express and computationally intensive.

Seeing the familiar formula, Dana looked embarrassed, but still nodded.

Claire still didn't know why, but she had the experience of the previous times, she suppressed the doubts in her heart, did not speak rashly to prevent being slapped in the face by Reiner, and listened attentively to Reiner's lecture.

"Dana, I think a large part of the reason why you failed to cast spells is because you went wrong when you built the spell model, I have a test paper here, I hope you will spend half an hour doing it."

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

The student took the test paper and quickly turned pale.

Because it's all math problems.

From basic arithmetic to complex equations for solving functions, there are ten questions on this paper, which is roughly equivalent to the level of high school students on Earth.

Dana glanced at Reiner, and there seemed to be resentment in her eyes.

Still, she picked up the quill on the table and began to work on the problem.

"So now we're waiting for her to finish?"

Claire asked in a whisper, Reiner shrugged, and handed Claire a piece of paper.

"Why don't you do it too?"

That's exactly the same question as Dana.

"Hmph, I'm not going to be fooled."

The same trick won't work twice, and Claire is naturally not afraid of Reiner's agitation.

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

In the triangle ABC, AB=2, AC=3, and angle A=60 degrees are known, and the length of BC and the value of sin2C are found.

“......”

"It's okay, there's no shame if you can't do it."

Reiner laughed, "This kind of problem is honestly quite difficult for a student like Dana, but the calculation of the geometric relationship on the plane is also necessary for the mages to build a model of the spell.

"Hmph, don't underestimate me!"

Claire glanced at Reiner, then picked up her quill and began to sketch, but it was clear that she was much faster than Dana.

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

Although Claire made a lot of mistakes and couldn't write the title, she still met the standard overall.

As for Dana, none of the questions were answered correctly, much to her frustration.

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

Dana muttered to herself.

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

Reiner's words caused the otherwise dejected student to slowly raise his head.