Professor Mike was a tolerant teacher. Though he noticed the friction between Lilith and Vina, he had no intention of intervening. To an old man like him, children's squabbles were amusing and harmless.
He had little hope that Lilith would be able to answer the question, as it was indeed challenging for them. Not being able to solve it was normal.
"Lilith, would you like to answer this question?" Professor Mike had already prepared himself for a refusal.
Lilith had already mentally calculated the answer. Hearing his question, she stood up and said, "The answer is the square root of three, approximately 1.7 inches."
"Not willing is also... Wait," Professor Mike's eyes lit up. "Say that again. What is your answer?"
Vina almost laughed out loud. Square root of three? Is that even an answer? Unable to do math and giving random answers would surely make Professor Mike angry. She looked at Lilith with pity.
Lilith ignored Vina and earnestly repeated to Professor Mike, "My answer is the square root of three, approximately 1.7 inches."
To be honest, she wasn't entirely sure because she didn't know how advanced mathematics was in this world. But medieval Europe did have square roots, though the terminology varied. "Square root of a number" was the most common term, so she used that instead of root three.
Professor Mike's eyes grew brighter. "You know how to calculate square roots and trigonometric numbers?"
It seemed her answer was correct. Lilith breathed a sigh of relief and modestly replied, "I was fortunate to have learned it and haven't forgotten."
"My child, you are too modest," Professor Mike praised. "I have taught many students, but most of them couldn't understand this and would just draw rigid diagrams."
Lilith maintained a polite smile, not sure how to respond.
Professor Mike grew more satisfied with her. "Good child, sit down." He then addressed the class, "Lilith's answer is correct. Did anyone else get it?"
Vina looked incredulous. How did Lilith know the answer? She hadn't even used the sand tray.
Unwilling to give up, Vina said, "Professor, aren't you going to ask Lilith how she calculated it? I didn't see her using the sand tray."
Hearing this, the students craned their necks to look at Lilith's sand tray.
"Really, there's nothing. Did Lilith calculate it in her head? Amazing!"
"Lilith must be a genius!"
"No wonder she's a noble lady..."
Vina ground her teeth. She had wanted them to doubt her, not praise her!
Professor Mike, disappointed with Vina, called on Lilith again. "Child, could you explain your thought process to everyone?"
Lilith nodded calmly. "First, calculate the distance from the center of the hexagram to its six vertices. Then, calculate the vertical distance from the intersection of the square's diagonals to its sides, which is the radius of the largest circle within the square. Finally, find the ratio between the two distances and use that to determine the reduced length of the hexagram's sides."
The classroom filled with the sound of pencils scratching on sand as students tried to replicate her calculations.
"So that's how it's done. I see now!"
Half the students looked enlightened, while the other half tugged at their hair in frustration. By the end, many were still puzzled. They knew the method, but how to calculate the distance from the hexagram's center to its vertices?
Seeing this, Professor Mike smiled slyly. "Can't figure it out? That's okay."
"This question was never meant to be solved by you. It was to introduce the mathematical concepts we will be covering next."
"Trigonometric numbers and square roots."
Students: !!!
They looked at Professor Mike in disbelief. "Professor, you're too mean!"
Professor Mike laughed heartily. "I am a humorous man. Now sit down, children, and let's continue the lesson."
The students sat up straight, focusing seriously on the blackboard. Even Vina sat down, her face dark.
She didn't understand. Lilith was clearly a commoner. How did she know so much? Could she really be a noble?
After class, Lilith left the classroom, followed by a persistent shadow. After a while, she turned around in exasperation. "Vina, what do you want?"
Vina looked at her with a complicated expression. "Are you really a noble? From which country, and what is your family's title?"
Lilith responded coldly, "Vina, asking such questions is very rude."
"Shut up!" Vina's face showed resentment, clearly remembering Lilith's scolding from the day before.
Lilith ignored her and headed towards the dining hall.
The midday sun was dazzling. Groups of cheerful boys and girls walked along the shaded path, chatting and heading to the dining hall together.
Clink, clink... copper coins scattered on the ground, some rolling into the grass along the sloped path.
"Ah!" A girl frantically bent down to pick up the coins, sweating in the flow of people. "Excuse me, please let me through. I dropped my coins... Please lift your foot, you're stepping on my coin... Thank you, I'm very sorry..."
A coin rolled to Lilith's feet, which she stopped with her foot. She picked it up and approached the girl. "Your..."
"Oh, I'm sorry, did I block your way?" Seeing a glimpse of a luxurious dress, the girl hurriedly stood up to make way. "I'm sorry, I didn't mean to."
Lilith pressed her lips together and handed out the coin. "I just wanted to say, this is your coin."
The girl looked up sharply, eyes wide with surprise.
Lilith also paused when she saw the girl's face. In the original owner's memory, this was the only person who had tried to give her water when she was hung on the city wall as a public display.
Those commoners, though also commoners, had shouted for her death.
Lilith's eyes darkened. She regained her composure and extended her hand further. "Don't you want it?"
The girl quickly wiped her hands on her clothes and respectfully took the coin with both hands. "Thank you, thank you very much!"
"No need to thank me," Lilith crouched down. "Let me help you pick them up."
"No, it'll dirty your dress," the girl said hurriedly, trying to stop her. "I'll do it myself."
"It's fine if it gets dirty." Lilith picked up coins from the grass, noticing the girl staring at her. "What's the matter?"
The girl, embarrassed, shook her head. "No, nothing. It's just that I've never met a lady as noble and kind as you."
Lilith paused for a moment, handing her the coin. "What's your name?"
The girl nervously straightened up. "My name is Winnie, Winnie Chali."
"I'm Lilith," Lilith extended her hand. "Winnie, can we be friends?"
"Of course!" Winnie held her hand to help her up, her eyes shining. "As long as you don't mind!"
Lilith blinked. She meant to shake hands, not be pulled up.
Oh well, it seemed handshakes weren't common among commoners.
"Did you find all the coins?" she asked.
Winnie counted and finally smiled. She gratefully thanked Lilith. "If it weren't for your help, I wouldn't have had enough money to rent a horse."
"Rent a horse?"
Winnie nodded. "I'm a mid-level magic apprentice. There's an entrance exam in two days, and I need to test my riding skills. I can't afford a horse, so I have to rent one."
"The academy doesn't provide horses for students?" Lilith worried because she couldn't afford a horse either.
"They do, but those horses are very old," Winnie explained. "The noble students use their own fast horses. If my performance is too poor, I'll lose my tuition exemption."
"There's a tuition exemption?" Lilith's interest was piqued, as she was also short on tuition money for next semester.
"Is it hard to get?" she asked casually.