Chapter 73

Lena vaguely remembers that his high school math teacher said that learning mathematics is clumsy, and people with inflexible thinking need to do a lot of training to develop their ability to calculate and solve problems. If they can't learn mathematics well, they have done less problems. Now, it's quite right.

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

One of the reasons Dana can't build the magic model is that she can't calculate the coordinates of the magic node and the function equation of the magic channel correctly, which leads to the failure.

The world's mages are not easy.

Lena thought that after he had tried to cast the spell, he found that just calculating the node position and Magic Channel trajectory of the zero ring spell would make his head bigger, which is equivalent to calculating the quadratic curve equation in mind. However, under the effect of magic, this process is very wonderful. Lena hardly took much effort to build it successfully. This calculation process seems instinctive. If he is skilled, he doesn't even know how to do it Too much awareness needs to be invested in this.

He hasn't experienced the casting process of more powerful mages yet. He speculates that those mages may be able to calculate high-order equations and differential equations in a short time, which can be regarded as humanoid computers.

In the face of the present problems, Lena thinks that only by improving Dana's mathematical level on the one hand, and by giving her better mathematical tools on the other hand, can she do it.

Pick up that paper, Lena will be compared with Claire, it is easy to see that Dana's mathematics is reflected in many aspects.

The first is the inflexible way of thinking, reflected in the geometry problem is not good at drawing auxiliary lines, curve problem can not change the conditions.

The second is computational power, which has some relative basis, but the amount of calculation is complex. Although Dana can find a way to solve the problem, there are mistakes in the calculation.

Finally, Lena realized that Dana seemed to have a little bit of self-confidence.

Due to the draft notes left on the test paper, it is clear that Dana's original idea is correct on some topics, but the result of calculation is very cumbersome, so she thinks she has miscalculated and missed the answer.

There are many reasons for this mentality. It may be due to inferiority complex caused by mistakes in the past, or it may be due to personality. More background information is needed.

But what makes Lena feel strange is that since Dana was born in a magic family, she has not been influenced and is very unfamiliar with the related magic, which is not normal.

While explaining the correct way of solving problems to Dana, Lena is thinking about these things. He is a teacher, and he can't help trying to teach the "poor student" well.

"You need a lot of training. If you don't have a good foundation, you'll have to redouble your efforts. From today on, I'll give you a similar paper every day. You come to my office after dinner and I'll answer it for you."

Lena said that Dana could not help fighting a cold war.

This paper has made her feel the terror of being dominated by mathematics. Now Lena asked her to write one every day. Is this person a devil?

In fact, it is much more difficult to write a test paper than to answer it simply. This is also to train his mathematical ability and prepare for passing the advanced examination.

At the same time, he can also test the effectiveness of this education method on Dana. If the effect is good, he may extend it to the whole crescent college.

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

Fortunately, the low-level mage doesn't need much mathematical skills, even calculus. Lena's current knowledge is more than enough.

"Can I have a few less questions..."

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

"In addition, besides the training of basic skills, the method of building a magic model is also very important."

Lena returns to the podium and refocuses Dana and Claire's eyes on the blackboard, the light model.

At the beginning, the words of Reiner's improved magic model reappeared in their minds. The two women looked at Reiner with a curious attitude, and they didn't know where he was going to improve.

But I didn't expect that Lena didn't continue to write on the magic model. Instead, he pointed the next point with white chalk.

"We have a new coordinate system."

Lena drew a straight horizontal line, set the origin as O and the horizontal axis as R. of course, these are not English characters, but two letters of common language.

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

"Why?"

Just when they were confused, Lena extended a line from the origin, and then marked the angle between the line and the horizontal axis, which was set as θ, and the point at the other end of the line was set as a.

"In the past, two values could be used to determine a point on the plane in the rectangular coordinate system. For example, if this point is in the rectangular coordinate system, it should be a (x, y). Assuming that X and y are both 1, then a should be (1, 1)."Said Lena, and the conversation turned.

"But if I don't use X and y, but instead use the angle θ and unit length r of the line between point a and the origin and the abscissa to represent this point, what would I get?"

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

A（r*cosθ，r*sinθ）。

This special way of expression made Dana a little dizzy, but trigonometric function was the foundation of magic. In magic, angle calculation was more convenient, so she soon understood it.

"This is a new method of coordinate expression introduced by me, which can be called polar coordinates."

With that, Lena established a normal rectangular coordinate system and drew an upward parabola through the opening of the origin.

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

He asked, taking Dana by surprise.

Fortunately, it's relatively simple. Dana gave the answer very quickly.

"Er, y = x ^ 2?"

"To be exact, it should be y = 2p * x ^ 2. In this functional equation, because it involves the operation of square, it is more complicated than the general linear equation. If the position of the curve changes, such as it is not at the origin, it will be more troublesome."

Said Lena, continuing to write on the blackboard.

"Next, we can establish two equations: y = R * sin θ, x = R * cos θ, and substitute them into the original equation. After elimination and simplification, we can get an equation, r = Tan θ 2p * cos θ."

Claire nodded, but the equation seemed more complicated. She didn't understand why Lena used this 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 bit, R is the distance between the point on the parabola and the focus, and θ is determined as the angle between the line between the point on the parabola and the focus and the positive direction of the vertical axis?"

Claire and Dana were stunned by Lena's question.

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