She took a deep breath, cald herself, and continued speaking.
"You ntioned before that we can use the 'path optimization equation' to verify Mr. Jas's conjecture. That is, when an object moves from one point to another, it chooses a path that minimizes a certain 'action quantity'."
"Initially, I couldn't understand what this 'action quantity' is, nor how to describe it in mathematical terms. But in your class, I was inspired by the energy conservation law you discussed."
She picked up a feather pen and quickly wrote a line of scribbled formulas on the draft paper, her bright eyes flashing with confidence.
"To quantify and calculate this idea of 'least effort', we need a mathematical tool to define the 'total cost' of a path. I define it as S, which is the kinetic energy T of the system at any given mont, minus its potential energy V."
"Then, the 'total cost' S of a system from ti t1 to t2 is the accumulation of the 'cost' at each mont during this period—integral!"
"Thus, the 'principle of least action' becos an extrely concise description—the actual path of motion of the system is the path that minimizes this S value!"
"And the thod to solve this 'function of a function' is precisely the variational thod you taught !"
[S=∫t1t2(T−V)dt]
Luo Yan looked at the formula on the draft paper, then at the girl beside him with shining eyes, feeling imnsely shocked.
Brilliant.
Don't be fooled by the simplicity of this formula, just one step further, and it's the Euler-Lagrange equation!
Although he had realized before that this girl was a genius, he hadn't expected her genius to reach this level.
"...This is a brilliantly genius idea, Ilana," Luo Yan sincerely praised, "I encourage you to continue exploring this path, my intuition tells ... you're not far from the main point."
"Mainly it's your inspiration..." Ilana said shyly with a smile, lowering her head, "If it were just my strength, I definitely wouldn't have thought of so much."
To be honest, she always suspected in her heart that her esteed ntor actually already knew the answer. Only he deliberately didn't say it, instead giving her the opportunity to discover the truth herself.
As for why he did this, she didn't know.
Luo Yan smiled faintly without speaking.
Holding a book of , Ophelia silently waited on the side, wanting to interject but not knowing where to begin.
She originally ca to ask Prince Colin about calculus, but she hadn't had a chance to speak after waiting a long ti.
The purely academic atmosphere made her feel like an outsider.
A faint sense of jealousy welled up in her heart, and she finally couldn't help but speak up, muttering softly.
"By Saint Sis, this is the Mage Tower... what does what you're talking about have to do with 'Magic Power'?"
"Of course, it has a relation."
Luo Yan turned to look at the confused eyes of the Duchess and patiently explained with a smile.
"Magic Power can also be understood as a type of 'force', or rather a type of 'action quantity'... it's just that we don't fully understand its nature yet."
Ilana's eyes widened slightly, and a trace of excitent surged in her heart. What Prince Colin said was exactly what she'd been pondering!
Sure enough—
She was now increasingly certain of her inner suspicion!
Prince Colin knows!
Listening to this groundless explanation, Ophelia pouted a little defiantly.
However, because the one who said this was, after all, the Prince she admired, she couldn't help but believe a little.
At this mont, a sudden rush of footsteps approached quickly, and Assistant Kegi ran into the laboratory like the wind.
Ignoring the other apprentices around, he quickly ran up to Luo Yan, breathlessly speaking.
"Mas...Master! Professor Hector urgently needs to see you, requesting you to go to his office imdiately!"
Luo Yan raised his eyebrows in surprise, seeing Kegi's anxious expression that didn't seem like a joke, he asked, "Is it urgent?"
Kegi nodded earnestly, his face stern.
"Yes! The professor's tone is extrely urgent! I asked what it was about, but he wouldn't reveal it to !"
Luo Yan nodded, ready to follow Kegi out.
However, just then, he noticed the in Ophelia's hands and her pitiful expression as she looked at him.
His heart moved slightly, and with a smile, he turned to Ilana and instructed her.
"Ilana, I have sothing to attend to. In my absence, the task of guiding Miss Ophelia is entrusted to you."
"You are her senior, and I trust this small task won't be very difficult for you."
Then he turned to Ophelia.
"You will study well, won't you?"
This sudden command struck like a flash of lightning, leaving both Ilana and Ophelia stunned, their expressions varied.
Ilana's eyes were filled with honored astonishnt, temporarily at a loss.
She felt extrely honored to have earned such trust from her Master, yet unprecedented pressure at the thought of teaching the Duke's daughter as a "teacher."
Would this... be overstepping?
Ophelia also felt at a loss.
But it wasn't due to concerns about overstepping, rather she hadn't expected the Prince would have her competitor guide her.
Admittedly, Ilana's abilities were well acknowledged by all apprentices in the laboratory, but was there no one else who knew calculus?
He clearly knew her feelings!
Not only that—
He certainly understood Ilana's feelings as well!
Ophelia blushed, hastily glancing at Ilana beside her, and eventually bit her lip and nodded.
"Yes... Prince, if it is your command."
Before leaving the Holy City, she silently swore in her heart that no matter what hardship and effort she had to endure, she would make Prince Colin acknowledge her charm.
If this was Saint Sis's test for her, then let the storm co with even greater force!
Incidentally, this line is from the second chapter of "Baron Cosia's Drifting Story"—The Undaunted Baron.
Watching Miss Ophelia's inexplicably reddening face, Ilana also nodded cautiously, softly saying.
"I will do my best… Master, and Duchess."
"Just call Ophelia!"
"Yes... Miss Ophelia."
Seeing the "harmonious (yet awkward)" relationship between the two, Luo Yan nodded in satisfaction, a smile of approval spreading across his face.
Very good.
Although the plan to "dissuade Miss Castellion" took a step back, the plan to "tie Miss Castellion to the Tower of Great Sage" made significant progress.
"Kegi, let's go and not keep Professor Hector waiting." Having resolved one affair, Luo Yan turned around, smiling as he spoke to Kegi.
"Ah... Yes, Master." A bewildered Kegi ca to his senses and quickly led the way ahead.
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