While Reiner and Dana are busy designing new uniforms, much to Claire's dismay, Reiner's paper on polar coordinates arrives on the judging panel.

The alchemy creature responsible for distributing the paper scanned the content of the paper, confirmed that the repetition rate was acceptable, and passed it to the audience of the three reviewers according to the extracted keywords.

One of them is Orb, a four-ring mage of the law system.

There have never been many mathematics-related papers, so there is neither a special office tower, nor a fixed review committee, and Orb's main research direction is magic circle, that is, the study of trying to rely on simplified spell models to optimize spellcasting, so the mathematical foundation is good, and this will be reviewed by mathematics-related papers.

He was not tall and had the same name as a mage from his fellow disciples, so he was also teased for a while as "Short Orb".

Awoke from his nap, pushed open the office door, and saw the papers that had been delivered at noon.

Unlike many unruly mages, Orb's desk is very neat, everything is arranged in a neat way, which may be the obsessive-compulsive disorder of mages who study circle science, and they must be neat before they can get to work.

He sat down, picked up the bottle in his hand, and took a sip of the black drink in it, the pungent gas made Orb suddenly refreshed, this gadget called Coke has recently begun to quietly become popular among the mages of the Rainbow Tower, and the unique taste is loved by these people who like novelties, and Orb is no exception.

The included mage card has also become a collector's item for some quirky mages, who are not resistant to this way of depicting the life of the mage, but some people even have the idea of writing letters to the manufacturer to make themselves into cards to increase their popularity, but Orb does not comment.

As he sipped his Coke and picked up the paper on his desk that was waiting to be reviewed, Orb saw the author of the paper.

Lionel. Ian Gray.

Poof-

Orb squirted out a mouthful of Coke, which immediately stained the neat desktop and the cover of the paper, but he didn't care so much at this time.

"Reiner. Ian Gray! ”

Another mage in decades who has caused the cognitive collapse of the judges with his thesis, uh, to be precise, the mage's apprentice, Reiner. Ian Gray's name spread in the Rainbow Tower when he won the Hohenheim Gold Cup as a young man and apprentice.

In the minds of many judges, the thesis of this mage apprentice should not be underestimated, and the slightest attention may lead to cognitive collapse.

Even because of the incident caused by Reiner, some of the jury called for the establishment of a sound protection mechanism to prevent the recurrence of such incidents.

Care for life, protect the judges, please support the key breakthrough paper pre-labeling bill.

Is it finally your turn?

Orb was furious and quickly threw the paper to the corner of the table, as if just one glance at the title of the paper would cause him to have a magical reversal.

It had been about five minutes, and only after Orb had calmed down did he dare to glance at the title of the paper.

"A new coordinate system and its ellipse, hyperbola, parabola and other curves under this coordinate system function equation study".

Coordinate system? Curve? Functional equations?

This is clearly a mathematical paper.

As Reiner learned, the number of papers in mathematics is very small, because there is no feedback, and most mathematical theories are just simplifications, so there are very few people who specialize in mathematics and publish papers.

Even Isaris, who is in the law system. His Excellency Alberton's calculus paper was only a supplementary chapter to describe the three laws of kinematics that he established.

What's more important is that since mathematics does not cause feedback from the world, and naturally does not cause cognitive collapse, Reiner's paper can be said to be safe and harmless.

"Thankfully, it's a paper on mathematics."

Orb relieved himself and picked up the paper that had been stained with Coke.

"A new coordinate system, though?"

Before opening it, Orb frowned slightly.

As we all know, Ander. The Loire Cartesian coordinate system proposed by Lord Loire is currently the most widely used coordinate system, and the application in many spell models has been affirmed.

Orb opened Reiner's paper with questions, and the neat format as usual pleased the meticulous circle mage, but when he saw Reiner's polar coordinates, he was silent.

With angles and radii as variables, it was clear that this coordinate system was better suited to describing curve equations, and Orb thought, as he continued to read, feeling more and more that this coordinate system seemed to be more suitable for some particular spell models.

"Eccentricity, the unity of the curve equation?"

When Orb read Reiner's polar equations for several common curves, the mage's hands trembled slightly.

Because in the end, Reiner's equation is so simple and elegant, full of a harmonious beauty.

That's exactly what mages like Orb are looking for, to build spell models in the most concise way possible, and to make the most of their magic!

Putting down the paper, Orb did not rush to write a review opinion, he picked up the calculation circle and began to verify the contents of the paper, and when he saw that as the eccentricity changed, the whole curve also changed as described in the paper, the mage stood up.

"W-This is wonderful!"

Orb muttered to himself, and he hurriedly sat down again, picked up his pen and paper, and began to perform polar coordinates conversion on the several spell models that were bothering him.

Time passed quickly, and by the time Orb raised his head, it was already sunset, and he found that polar coordinates had a natural advantage in certain spell models, and in other spell models they were more cumbersome, and if they were complementary to the original Cartesian coordinate system, then many spell models that were considered difficult to simplify in the past could be further optimized.

For high-level mages, this kind of optimization is meaningless, it is just a subtle increase in casting efficiency, but for mid-level mages and low-level mages, such an optimization is quite rare, at least judging from the spells in Orb's hands, the casting efficiency of mid-level mages has increased by ten to twenty percent, and low-level mages have more!

Orb was still immersed in calculations, and out of the corner of his eye, he stumbled upon a book on the Three Laws of Kinematics, calculus was too difficult for an intermediate mage like him to understand, and the calculations were even more complicated than common sense.

He suddenly had a bold idea, what would happen if polar coordinates were applied to calculus?