Greetings, Mister Principal

One of the reasons why Dana could not successfully construct the spell model was that she could not correctly calculate the coordinates of the spell node and the function equation of the magic channel, resulting in deviations, which led to failure.

It made Reiner realize that being a mage was really not easy in this world.

After trying to cast the spell himself, he found that just calculating the node position and magic channel trajectory of the zero-ring spell was daunting. It was like doing the quadratic equation in his head, but under the action of magic, the process was very miraculous. So Reiner could complete it successfully with little effort. This calculation process seemed instinctive. If he was proficient, he didn't even need to put too much attention to it.

Reiner guessed that maybe those high-level mages could mentally calculate other equations such as differential equations in a short time. They could even be regarded as humanoid computers.

Leaving aside these issues, Reiner believed that to solve Dana's problem, he needed to improve Dana's own mathematics level and also give her better mathematical tools.

Picking up the test paper, Reiner compared it with Claire, and it was easy to see Dana's math problems manifest themselves in many ways.

The first was that her way of thinking was not flexible, which was reflected in the geometry problem. She was not good at drawing auxiliary lines and was unable to do conversions in curve problems.

The second was her calculating ability. When it came to some relatively basic but complex calculations. Although Dana could find a solution to the problem, there were errors in the calculations.

In the end, Reiner noticed that Dana seemed to also lack confidence.

From draft notes on the test paper, it could be seen clearly that Dana's original ideas were correct on some topics, but because of the cumbersome calculations, she either thought it was wrong, or she couldn't complete the calculation.

There were many reasons for this mentality. It may be due to low self-esteem caused by mistakes in the past, or it may be due to personality, which required more background information.

But what made Reiner feel strange was that Dana was clearly born in a mage family, but she was very unfamiliar with some magic, which was abnormal.

Reiner explained the correct way to solve the problem while thinking about these things. He was a teacher. At this time he couldn't help but want to teach the "bad student" before him.

"You need a lot of training. Since your foundation is not as good as others, you will have to work harder. Starting today, I will arrange a similar test paper for you every day. After you finish the test, you can come to my office after dinner. I will give answers."

Hearing what Reiner said, Dana couldn't help but shudder.

This test paper had already made her feel the horror of being dominated by mathematics. Now Reiner wanted her to take one every day. Was this person a demon?

Actually, it was much more difficult to produce test papers than simply answering the test papers. Reiner was also using this opportunity to exercise his mathematical ability and prepare for the advanced exam.

At the same time, he could also test whether this educational method was effective on Dana, and if it worked well, he may extend it to the entire Luna Nova Magical Academy.

After all, the percentage of successfully advanced mages was also part of the annual assessment of an academy.

Fortunately, the mathematics required by the low-level mages was not so deep, so Reiner's current knowledge was more than enough.

"Can you make fewer questions..."

Dana asked timidly, but Reiner flatly refused the request, which made the girl lament.

"In addition, apart from basic skills training, the method of constructing spell models is also very important."

Reiner returned to the podium, so that Dana and Claire's eyes once again focused the spell model of the Illumination on the blackboard.

In the beginning, what Reiner said about improving the spell model resurfaced in their minds again. The two women looked at Reiner with curiosity, wondering where he wanted to start improving.

Unexpectedly, Reiner did not continue to write on the spell model but use white chalk to draw a point next to it.

"Let's create a new coordinate system."

Reiner drew a straight horizontal line, and set the origin as o and the horizontal axis as r. Of course, this was not an English character, but two letters of the Common Language in this world.

But then, Claire's expected vertical axis did not appear, as if Reiner's coordinate system ended here.

"Huh?"

Just when the two were puzzled, Reiner extended a line from the origin, and then marked the angle between this line and the horizontal axis, and set it as θ, and the other end of the line as a.

"In the past, a Loire coordinate system can use two values to determine a point on the plane. For example, if this point is in a Loire coordinate system, it should be a (x, y). If x and y are both 1, then a should be (1, 1)."

Reiner looked and the two and carried on,

"But if I don't use x and y, but instead use the angle θ between the line of point a and the origin and the abscissa axis and the length r to represent this point, what will be the result?"

After giving them some time to think, Reiner continued to write on the blackboard.

a（r*cosθ，r*sinθ）。

This special way of expression made Dana a little dizzy, but trigonometric functions were the foundation of magic. In magic, angle calculations were also more convenient, so she quickly understood.

"This is a new coordinate expression method that I introduced, which can be called Polar Coordinates System."

After finishing speaking, Reiner established a normal Loire coordinate system next to him, and drew a parabola with the opening upward passing through the origin.

"If we want to describe the functional equation of this curve, what should it be, Dana?"

He asked, catching Dana off guard.

Fortunately, this was relatively simple, and Dana quickly gave the answer.

"Uh, y=x^2?"

"To be precise, it should be y=2p*x^2. In this functional equation, due to the operation of squaring, it is more complicated than the general straight-line equation. If the position of the curve changes, such as not at the origin, it will be more troublesome. "

Reiner said, and continued to write on the blackboard.

"Next we can establish two equations: y=r*sinθ, x=r*cosθ, substituting them into the original equation, and after eliminating the simplification, we can get an equation, r=tanθ/cosθ."

Claire nodded, but the function equation seemed more complicated. She didn't understand why Reiner used this troublesome way to record the trajectory of the curve.

"Of course, this is a very complicated way, but what if we slightly change the definition, for example, r is the distance between a point on the parabola and the focal point, and θ is determined to be the angle between the point on the parabola and the focal point in the positive direction of the vertical axis?"

Reiner's question stunned Claire and Dana