Greetings, Mister Principal: Reiner’s Mathematics Classroom (Part 1)

Reiner vaguely remembers his high school mathematics teacher saying that when learning mathematics, the stupid bird flies first. People with inflexible thinking need to do a lot of training to develop their ability to calculate and solve problems. If you are not good at mathematics, you will be able to solve the problems well. Shao, now that I think about it, this is quite correct.

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

One of the reasons why Dana was unable to successfully construct the spell model was that she could not correctly calculate the coordinates of the spell nodes and the functional equation of the magic channel, resulting in a deviation, which led to the failure.

It’s not easy for mages in this world either.

Reiner thought to himself that after he tried casting spells himself, he found that just calculating the node position and magic channel trajectory of the zero-ring spell was a headache. This is equivalent to mentally calculating the quadratic curve equation, but under the influence of magic power, This process is very wonderful. Reiner succeeded in constructing it with almost no effort. This calculation process seems to be instinctive. If he is proficient, he does not even need to invest too much consciousness in it.

Having not experienced the spellcasting process of more powerful mages, Reiner speculated that maybe those mages can mentally calculate high-order equations and differential equations in a short time, and can be regarded as humanoid computers.

Putting these aside, facing the problem at hand, Reiner believed that the only way to improve Dana's mathematics level on the one hand, and to give her better mathematical tools on the other hand.

Picking up the test paper, Reiner compared it with Claire. It was easy to see that Dana's math differences were reflected in many aspects.

First of all, the way of thinking is not flexible, which is reflected in the inability to lead auxiliary lines in geometry questions and the inability to change conditions in curve questions.

The second is calculation ability, which is relatively basic but requires complex calculations. Although Dana was able to find a way to solve the problem, she made mistakes in her calculations.

Finally, Reiner noticed that Dana still 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 questions, Dana’s original ideas were correct, but because the calculated results were very cumbersome, she thought she had made a mistake. , thus missing the answer.

There are 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. More background information is needed.

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

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

"You need a lot of training. If your foundation is not as good as others, you have to work twice as hard. From today on, I will assign a similar test paper to you every day. You come to my office after dinner. , I will give you the answer."

Reiner said, making Dana shudder.

This test paper has 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 devil?

But this is not Reiner's evil deed. In fact, writing test papers is much more difficult than simply answering them. Reiner is also doing this to exercise his mathematical skills and prepare for passing the advanced examination.

At the same time, he can also test whether this educational method is effective on Dana. If the effect is good, he may extend it to the entire Crescent College.

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

Fortunately, the mathematics skills required for low-level mages are not very deep, and they don't even need calculus. Reiner's current knowledge is more than enough.

"Can I skip a few questions..."

Danna asked timidly, but Reiner flatly refused the request, making the girl lament.

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

Reiner returned to the podium, causing Dana and Claire to focus their eyes on the blackboard again, the illumination spell model.

What Reiner said at the beginning about improving the spell model came to their minds again. The two ladies looked at Reiner with curiosity, not knowing where he would start improving it.

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

"We create a new coordinate system."

Leiner drew a straight horizontal line, setting the origin as O and the horizontal axis as r. Of course, these are not English characters, but two letters of the common language.

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

"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, which was designated as θ, and the point at the other end of the line segment was designated as A.

"In the past, the Cartesian coordinate system could use two values ​​to determine a point on the plane. For example, if this point was on the Cartesian coordinate system, it should be A (x, y). Assume that x and y are both 1, Then A should be (1, 1)."

Reiner said, then changed the subject.

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

After giving the two of them some time to think, Reiner continued writing on the blackboard. ~IndoMTL.com~.

This somewhat special way of expressing it made Dana a little confused, but trigonometric functions are the basis of magic. In magic, the calculation of angles is also more convenient, so she quickly understood it.

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

After speaking, Reiner established a normal rectangular coordinate system next to it and drew a parabola passing through the origin and pointing upward.

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

He asked, catching Dana off guard.

But fortunately, this is relatively simple, and Dana quickly gave the answer.

"Uh, y=x^2?"

"To be precise, it should be y=2p*x^2. In this function equation, because it involves square operations, it is more complicated than the general straight line equation. If the position of the curve changes, such as If it’s not at the origin, it will be even more troublesome.”

Reiner said and continued writing on the blackboard.

“Next we can establish two equations: y=r*sinθ, x=r*cosθ, substitute them into the original equation, and after elimination and simplification, we can get an equation, r=tanθ/2p*cosθ. ”

Claire nodded, but the function equation seemed to be more complicated. She didn't understand why Reiner used 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 slightly, r is the distance between the point on the parabola and the focus, and θ is determined as the angle between the point on the parabola and the focus line in the positive direction of the vertical axis. Where are the horns?"

Reiner's question stunned Claire and Dana.