Reiner vaguely remembers that his high school math teacher said that learning math is a stupid bird flying first, and people with inflexible thinking need to do a lot of training to develop their ability to calculate and solve problems.

Of course, the math teacher later added that smart birds fly higher and faster, and that's another story.

One of the main reasons why Dana was unable to successfully construct the spell model was that she could not correctly calculate the coordinates of the spell node and the function equation of the mana channel, which caused a deviation, which led to the failure.

It's not easy to be a mage in this world either.

Reiner thought to himself, after he tried to cast the spell himself, he found that just calculating the node position and magic channel trajectory of the zero ring spell was a big head, which was equivalent to a mental arithmetic quadratic curve equation, but under the effect of magic, this process was very wonderful, Reiner almost didn't take much effort to build it, this calculation process was like instinct, if he was skilled, he didn't even need to put too much consciousness into it.

Having not yet experienced the casting process of a more powerful mage, Reiner speculated that maybe those mages would be able to mentally calculate higher-order equations and differential equations in a short period of time, and could be regarded as humanoid computers.

Putting that aside, Reiner believes that the only way to improve Dana's own math skills is to improve her math skills and give her better mathematical tools on the other.

Picking up that paper, Reiner compared it to Claire, and it was easy to see that Dana's math difference was reflected in many ways.

The first is that the way of thinking is not flexible, which is reflected in the fact that geometry problems are not good at leading auxiliary lines, and curve problems cannot change conditions.

The second is computational power, which has some relatively basic, but complex calculations, and although Dana can find a solution to the problem, there are mistakes in the calculations that lead to errors.

Eventually, Reiner sensed that Dana seemed to be hiding a hint of unconfidence.

Since the draft notes were also left on the test paper, it was clear that on some of the questions, Dana's original thinking was correct, but because the results of the calculations were very cumbersome, she thought that she had miscalculated and missed the answers.

There are many reasons for this mentality, it can be low self-esteem due to mistakes in the past, or it can be due to personality and need more background information.

But what makes Reiner strange is that since Dana was born into a family of magic, she has not been exposed to it, and she is very unfamiliar with related magic, which is not normal.

Reiner was thinking about these things while explaining the correct way to solve the problem to Dana, he was already a teacher, and he couldn't help but want to teach the "bad student" in front of him well.

"You need a lot of training, if the foundation is not as good as others, you have to work twice as hard, from today onwards, I will assign you a similar test paper every day, you come to my office after dinner, and I will answer for you."

Reiner said, sending Dana shudder.

This test paper has already made her feel the horror of being dominated by mathematics, and now Reiner actually wants her to write one every day, is this person a demon?

But this is not Reiner's evil behavior, in fact, it is much more difficult to produce the test paper than to simply answer the test paper, and Reiner is also to exercise his mathematical ability and prepare for passing the advanced exam.

At the same time, he can also test the effectiveness of this educational method on Dana, and if it works, he may be able to spread it to the entire Crescent Academy.

After all, the percentage of successful advanced mages is also part of the annual assessment.

Fortunately, the low-level mages didn't need much mathematical skills, not even calculus, and Reiner's current knowledge was more than enough.

"Can you miss a few questions......

Dana asked timidly, but Reiner flatly declined the request, causing the girl to lament.

"In addition, in addition to the training of basic skills, the method of building a spell model is also very important."

Reiner returned to the podium, and Dana and Claire's eyes were once again focused on the blackboard, the illuminator spell model.

Reiner's initial words about improving the spell model came back to their minds, and the two ladies looked at Reiner with curiosity, wondering where he was going to start improving.

Unexpectedly, Reiner did not continue to write on the spell model, but dotted a dot with white chalk on the side.

"We're building a new coordinate system."

Reiner drew a straight horizontal line, setting the origin point as an O and the horizontal axis as R, which of course is not an English character, but two letters of the lingua franca.

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

"Huh?"

Just when the two were confused, Reiner extended a line segment from the origin, and then marked the angle between the line and the horizontal axis, set it as θ, and set the point at the other end of the line segment as A.

"In the past, Cartesian coordinate systems can use two numerical values to determine a point on a plane, for example, this point, if it is in a Cartesian coordinate system, it should be A(x,y), assuming x and y are both 1, then A should be (1,1)."

Reiner said, then shifted.

"But instead of x and y, I use the angle θ between the line connecting point A and the origin point and the angle θ and the unit length r of the abscissa axis to represent this point, what will I get?"

The two of them were given some time to think before Reiner continued to write on the blackboard.

A（r*cosθ，r*sinθ）。

This was a bit of a dizzy way for Dana, but trigonometry was the foundation of magic, and in magic, the calculation of angles was also more convenient, so she quickly understood.

"This is a new way of expressing coordinates that I introduced, which can be called polar coordinates."

With that, Reiner established a normal Cartesian coordinate system next to it, drawing a parabola pointing upwards through the opening of the origin.

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

He asked, catching Dana off guard.

But fortunately, it 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, because it involves the operation of squares, it is more complex than the general straight line equation, and if the position of the curve changes, such as not at the origin, then it will be more troublesome."

Reiner said, continuing to write on the blackboard.

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

Claire nodded, but the equation seemed more complicated, and she couldn't understand why Reiner had to use such a troublesome way to record the trajectory of the curve.

"Of course, this is a very complicated way, but if we change the definition a little, r is the distance between the 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 longitudinal axis?"

Reiner's question stunned Claire and Dana.