APSIL -Chapter 95 The Ge Family Handbook of Mathematical Terms

Inside the study at the Ge residence, with the troublesome Emperor finally gone, Ge Yong stared at Zhang Shou. The annoyed expression from moments ago had completely vanished, replaced by a broad, pleased smile.

He even reached out and rubbed Zhang Shou’s head as if teasing one of his own grandsons. When his youngest disciple awkwardly ducked away, Ge Yong merely chuckled.

“You caused quite a stir by cleaning out Jiuzhang Hall last night. You’ve offended plenty of people in the Imperial College. But when someone accused Zhou Xun today, you didn’t seize the opportunity to kick him while he was down over a personal grudge. Instead, you cleared yourself of suspicion and even left Zhou Xun owing you a favor. Well done. You didn’t disgrace your old teacher.”

“And although you lied to His Majesty, it was out of good intentions, and you even knew to submit a confession afterward. That more or less makes up for it.”

Zhang Shou silently thanked his lucky stars.

Back at the Imperial College, although he had sensed that the Emperor hadn’t noticed the flaw in his story, he’d fully intended to ask Ge Yong to deliver a written confession on his behalf afterward. Better safe than sorry.

Feeling that anything he said now would sound self-congratulatory, he could only respond with an embarrassed laugh.

Fortunately, Ge Yong had no intention of dwelling on the matter.

What truly interested him was Zhang Shou’s method for determining whether the plaque was hollow.

“Since His Majesty asked me to verify whether the Imperial Ancestor’s plaque contains a hidden compartment, I first need to understand the principles behind your method. If it truly works, then using it merely on a wooden plaque would be wasting it. It would be far more useful for determining whether people have adulterated gold or silver ingots during casting. Come, explain how you came up with it.”

Zhang Shou could only smile awkwardly.

Wasn’t Archimedes’ principle itself supposedly discovered while trying to determine whether a king’s crown was pure gold?

After a moment’s thought, he decided to explain it carefully.

“Teacher, whether it’s petrified wood, gold, or silver, objects made from the same material and having the same weight should occupy the same volume. However, unlike the regular geometric solids described in The Nine Chapters on the Mathematical Art—such as the yangma and bienao—their shapes are irregular, making their actual volume impossible to calculate directly.”

As a recognized master of mathematics, Ge Yong immediately understood.

“Makes sense. Go on.”

“Since we can’t calculate the volume directly, we need another method of comparison. Water provides a convenient standard. Objects of the same volume displace the same amount of water when submerged. By marking the water level on the side of a tank, we can compare their actual volumes…”

As he explained, Zhang Shou realized that to fully clarify the principle, mathematics alone wasn’t enough.

Basic physics concepts—mass, density, volume, buoyancy, and so on—would eventually need standardized terminology. Otherwise, explaining it later to people less mathematically inclined than Ge Yong would become incredibly cumbersome.

The same applied to the archaic terminology in The Nine Chapters.

It would be far better if Ge Yong published a handbook introducing intuitive terms like square, rectangle, cube, rectangular prism, triangular pyramid, and square pyramid, rather than forcing everyone to memorize obscure names like yangma and bienao.

Just as Vice Director Luo, Old Black Xu, and those Imperial College doctors had demonstrated, most people had no idea what those ancient terms even meant.

Ge Yong suddenly nodded in realization.

“Excellent. I understand now. If the plaque had been made of a softer wood, such as nanmu, things would have been much more troublesome. We’d have needed to tie a heavy weight to it before submerging it.”

“Of course, this method can’t guarantee perfect accuracy. At best it’s approximately correct. When an object enters the water, it splashes. When it’s lifted out, water clings to it. Even the level markings themselves can’t be perfectly precise.”

“Teacher is absolutely right.”

Zhang Shou smiled, then couldn’t suppress another yawn.

“I’ll arrange for the test as soon as possible to determine whether the Imperial Ancestor’s plaque truly contains a hollow compartment…”

He paused.

“To be honest, I doubt it does.”

I think so too, Zhang Shou thought.

Otherwise, why would the Imperial Ancestor have left an entire room full of his calligraphy in the palace archives for generations to treasure?

With business concluded, Ge Yong snorted in dissatisfaction.

“Oh, right. Little Ying came with the Emperor earlier, but I chased her away. Last night she arranged for your mother to stay at Old Qi’s residence.”

He huffed.

“That ungrateful little girl!”

Learning that his mother hadn’t stayed at the Duke Zhao Mansion, Zhang Shou felt deeply grateful toward the seemingly carefree Zhu Ying.

He himself, having lived two lifetimes, wouldn’t have cared much about the prestige or wealth of Duke Zhao’s household.

His mother, Madam Wu, was another matter entirely.

For Zhu Ying to have thought of something so delicate was genuinely considerate.

Changing the subject, Zhang Shou quickly asked, “Teacher, where are A-Liu, Xiao Qi, and Xiao Dai?”

Ge Yong answered listlessly, “They’re outside. I told people to take them to the guest rooms, but those two insisted on waiting outside with A-Liu. Clearly they were worried about you.”

Zhang Shou immediately hurried outside and brought all three back into the study.

Before he could properly introduce Deng Xiaodai to Ge Yong, another snort interrupted him.

“Enough with that.”

“I’ve met Xiao Qi before. I’ve met Xiao Dai too. Otherwise, how would I have known there was a disciple like you hidden away in Rongshui Village?”

“The last time I was at Qingfeng Xulai Hall, I noticed that the youngest son of the Lu family seemed to possess some talent for mathematics. But from what His Majesty told me today, it’s far more than ‘some talent.’ Your luck is unbelievable!”

He looked positively indignant.

“It infuriates me! I have countless students in name, yet aside from you, and Wang Datou—the Prefect of Shuntian, who’s half my disciple—I can hardly find anyone gifted in mathematics.”

“And even those with talent are all busy pursuing official careers.”

“But you?”

“You somehow stumbled across three of them with hardly any effort!”

Zhang Shou hadn’t expected the teacher whose students filled the empire to actually envy his luck with disciples.

All he could do was smile.

Yet Ge Yong suddenly remembered something else concerning Wang Datou and immediately pointed accusingly at his wayward disciple again.

“Wang Datou sent someone to deliver me a message this morning.”

“He said that he summoned Xiao Dai last night, and the boy presented him with something called a bar chart and a line graph, claiming they made statistics like taxation, population, income, and expenditures far more intuitive.”

“Those were your ideas too, weren’t they?”

“Whenever you invent something new, couldn’t you show your teacher first?”

“Are you addicted to acting first and informing me afterward?”

I simply didn’t have time!

I returned to the village yesterday evening.

How could I have guessed that a mere clerk like Deng Xiaodai would be summoned personally by the Prefect? Or that Xiao Dai would move so quickly?

Though these thoughts ran through his head, Zhang Shou could only helplessly glance at the guilt-ridden Deng Xiaodai before obediently enduring another lecture.

In the end, he hastily promised that in the future, whenever he had a new idea, he’d consult his teacher first.

Only then did Ge Yong finally feel satisfied.

He let out a contented sigh.

When Deng Xiaodai nervously asked permission to return to the Shuntian Prefecture office, and Qi Liang likewise requested to go check on how Madam Wu had settled in, Ge Yong generously waved them off.

As for A-Liu, who stood silently in the corner like a wooden statue, Ge Yong merely glanced at him and ignored him completely.

“A-Shou.”

“Remember this.”

“In the future, whether it’s people or objects connected with the words Imperial Ancestor, stay as far away from them as possible.”

“This incident with the plaque doesn’t count—you were dragged into it for no reason.”

Zhang Shou hadn’t expected such a warning.

He was just about to ask why when Ge Yong deliberately cleared his throat and abruptly changed the subject.

“As for Xiao Qi’s placement in the prefectural examination—if Wang Datou hadn’t fiercely argued his case before His Majesty, plenty of people would have slandered him.”

“No one knows how long arithmetic will remain part of the prefectural examinations.”

“So whether you can establish yourself firmly at the Imperial College is extremely important.”

“That’s why I was so pleased with how you handled today’s events.”

“Wang Datou has excellent mathematical talent. You can consider him your senior fellow disciple.”

“Once Xiao Dai returns, he’ll certainly tell Wang Datou everything about today’s affair with the Imperial Ancestor’s plaque.”

“Heh! Compared with those line graphs and bar charts, this method for detecting hollow objects or impurities is much more interesting.”

Zhang Shou couldn’t help laughing.

Teacher…

I was waiting for you to explain the warning about the Imperial Ancestor.

Instead you’ve wandered off talking about arithmetic entering the examinations, my footing at the Imperial College, and Wang Datou?

That subject change couldn’t have been more obvious!

After a moment’s thought, he decided not to pursue the matter.

Instead, he smiled sincerely.

“Teacher, last night in Jiuzhang Hall, Lu Sanlang used the terms yangma and bienao from The Nine Chapters on the Mathematical Art to stump Vice Director Luo, several Imperial College doctors, and Supervisor Xu from the Discipline Office.”

“Although they were unfamiliar with arithmetic, another problem is that the terminology in the mathematical classics is far too obscure.”

He paused before continuing with a cheerful smile.

“Teacher, would you be willing, in your capacity as a grand master of mathematics, to publish a Ge Family Handbook of Simplified Mathematical Terminology and Symbolic Notation?”

Hearing this, Master Ge’s eyes lit up.

Then he shot his youngest disciple a meaningful look.

If I refuse…

You’ll just publish it under my name after the fact anyway, won’t you?

Snorting, he feigned indifference.

“Fine.”

“Tell this old man what you’ve got in mind first.”