An equation is simply an equality containing an unknown variable, X.
It is not some profound point of knowledge, but rather a simple calculation tool.
Solving through equations eliminates the difficulty of reverse thinking; one needs only to list the equality containing the quantity to be solved for in a direct manner.
Regarding the application of basic equations, the most widespread example is the problem of 'chickens and rabbits in the same cage'.
Dark merely explained the knowledge points he knew quickly, and Professor Lily achieved instant enlightenment!
She quickly said, "Similar methods were mentioned in the 'Geniro Canon', but they were not compiled into a system. Using this method can indeed simplify calculations. Although I don't need it... emmm, can you go deeper? Tell me more?"
Dark asked curiously, "What is the 'Geniro Canon'?"
Professor Lily replied, "An ancient sect that worshipped geometry. They have probably turned to ash by now."
The corner of Dark's mouth twitched. "A math religion?"
Subsequently, he complied with Professor Lily's request and went a bit deeper.
"Equations take many forms. What I just explained was a linear equation in one variable. Besides that, there are linear equations in two variables, quadratic equations in one variable, and so on. They can also form systems of equations to solve for multiple unknowns..."
And when speaking of quadratic equations, one inevitably has to discuss involution, or 'powers'.
With the definition of 'powers', one must then mention 'bases', 'exponents', 'roots'...
Dark spoke fluently, and Professor Lily listened earnestly. A basic model regarding mathematical operations gradually took shape amidst their exchange.
The further it went, the more shocked Professor Lily felt inside.
Starting from the introduction of the concept of 'powers', she discovered that some extremely complex calculations, after applying 'powers', were as if a straight road had suddenly been folded, causing the starting point and the endpoint to suddenly become close!
Clearly, this was a concept far above addition, subtraction, multiplication, and division!
Professor Lily originally just wanted to fish a method like 'vertical calculation' out of Dark, but she hadn't expected to obtain something even more incredible.
She pondered carefully, then suddenly took a pen and paper from her drawer. She wrote out various complex problems out of thin air, introduced the concept of 'powers', and then solved them using equations. The entire train of thought was as smooth as silk, unbelievably satisfying.
"So smooth!"
She raised her head, her face flushed with rosiness, only to discover that the person was no longer on the sofa.
...
In order not to attend the afternoon History of Magic class on an empty stomach, Dark chose to quit while he was ahead halfway through and slipped away.
Seeing Professor Lily able to infer other things from one fact and achieve mastery just by understanding a few definitions, Dark was actually somewhat envious. Perhaps that was what a true genius was!
Arriving at the cafeteria, he ordered a steak and a meat pie, ate quickly in the empty hall, and then hurriedly rushed to the History of Magic classroom.
When he entered through the back door, the classroom was already full of people.
Virt and Robert, sitting by the back door as usual, looked over curiously, surprised that he had arrived so late.
However, Virt already harbored some hostility toward Dark in his heart and had given up on his plan to increase favorability, so he did not strike up a conversation.
Robert, however, didn't have such reservations. He immediately said, "Hey, Dark, where have you been? Arriving just now."
Dark turned his head and smiled slightly. "I was discussing some problems with Professor Lily."
Robert: "Oh."
Virt still couldn't help but ask, "Is it related to the class this morning?"
"Yes." Dark nodded, then continued forward, quickly returning to his seat.
Not long after, the class bell rang.
The History of Magic professor—Ryan Hacks—walked in leaning on a cane.
He was still wearing a tattered prosthetic limb and walked with a limp, but the expression between his brows and his entire temperament were vastly different from when he first arrived.
Just one week of academy life had allowed him to shed the thick aura of twilight and decay, and a bit of toughness had returned to his brow.
But what attracted the students the most was his almost bald head—it had grown hair!
"Professor!"
A Knight House student in the front row couldn't help raising his hand. "Your hair?!"
Professor Ryan Hacks raised his intact hand, brushed his dark brown bangs back, and looked slightly smug. "Theodore, you need to relearn what manners are."
"Okay, Professor," Theodore muttered, sitting down with a pout.
Professor Hacks then said, "I just cooperated with Sister Carian on an experiment. Oh, she calls that stuff 'Hair Growth Potion'!"
"So he was a guinea pig..."
Dark, in the very last row, blinked, feeling that Professor Hacks shouldn't rejoice too early.
If a hair growth potion could be researched so easily, there wouldn't be so many bald heads among those great nobles.
However, with a head of thick brown hair and after shaving off his beard, Professor Hacks really did have the flavor of an old handsome man.
After Professor Hacks walked up to the podium, he continued the content from the last lesson, narrating the unfinished war stories.
Unfortunately, when the 'Golden Generation' headed by the Hero and others was active on the battlefield, Professor Hacks had already retired due to injury. Although he had detailed knowledge of those battles he didn't personally experience, he ultimately lacked some details.
So, he spoke more about the early battles. In those times, humanity had no advantage. Every victory required a heavy price, but the significance of every victory was also unprecedentedly great.
However, Professor Hacks had talked about victorious battles in the previous two lessons.
In this lesson, he seemed to have changed his train of thought.
Fifteen minutes after the class started.
Professor Hacks said, "Having both victory and defeat, that is war. We gain experience from victory and learn lessons from failure. The so-called history of war is also a history of sacrifice. I will always remember the comrades who sacrificed themselves, and I will never forgive the traitors in the war!"
He seemed to think of something and hurriedly covered the ferocity at the corner of his mouth with his fist, then calmed his breath before continuing.
"The Ghost Bull Tribe Defense Battle! That was a mournful cry in modern war history, a sorrowful battle that nearly caused the Alliance to fracture!"
The students below couldn't help but focus their attention.
Professor Hacks always carried strong personal emotions when lecturing, but that actually made it more engaging.
Even Dark couldn't help but listen intently.
The Ghost Bull Tribe Defense Battle was a campaign that occurred in the early period of the signing of the 'Alliance of Hundred Races Treaty'.
The Ghost Bull clan among the Beastman tribes sent a distress call to the Alliance at that time.
After urgent discussions, the Alliance immediately treated it as a key battle symbolizing the alliance, thereby dispatching an Allied Army composed jointly of the four major races: Beastmen, Elves, Dwarves, and Humans, to go to the Ghost Bull territory for rescue.
And Professor Hacks was right there among them!
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