"Construct a regular heptadecagon using only a compass and straightedge!"
Before anyone else could react, Cheng Jinzhou froze in place.
He swore by his dubiously obtained doctoral degree—this problem definitely wasn't something the old matriarch had come up with herself.
Don't think constructing a regular heptadecagon is easy. Before the 18th century, this was a world-class mathematical challenge, and a profoundly significant one at that.
These past few days, Cheng Jinzhou had been immersing himself in geometry books. Though his family's collection on the subject was limited, it gave him a glimpse into this world's mathematical capabilities.
Their level might approach early 16th-century Europe, perhaps even surpassing it in some areas. But researching how to construct a regular heptadecagon? That, in many ways, exceeded the limits of this era.
Compass-and-straightedge construction meant using only an unmarked ruler and compass a finite number of times to create geometric figures. The "finite" constraint specifically ruled out trial-and-error methods.
This was a problem that appeared simple but was deceptively complex. In the history Cheng Jinzhou knew, it was ultimately solved by Gauss—another mathematical genius whose contributions were too numerous to count. The least squares method that plagued engineering students and the normal distribution curve familiar to liberal arts majors were both his creations. But what made Gauss most famous among common folk was probably the arithmetic problem he solved at age nine or ten: 1+2+3+...+100.
In the 21st century, any child exposed to math Olympiads might not know Gauss by name, but ask "What's the sum from 1 to 100?" and most would instantly reply "5050" without calculation.
Gauss began researching the heptadecagon construction after entering university. How long it took him, Cheng Jinzhou couldn't recall, but it certainly exceeded twenty minutes. In other words, unless the Great Xia Dynasty's astrologers had mathematics a century more advanced, this was impossible.
Mathematics progressed step by step—like building a fortress on sand. One could develop unique methods, but never skip foundational steps. A mathematical formula missing even one proof was simply wrong.
Cheng Jinzhou believed if the astrologers commonly understood heptadecagon construction and related theories, they'd have already entered an industrial society—which clearly wasn't the case.
At this point, twenty minutes became meaningless. The matriarch likely intended for both children to fail.
A clever approach—it preserved the Long Branch's dignity while securing victory. The only issue was Cheng Jinzhou's irritation.
Had the matriarch been less shrewd, pitting him against a child in mathematics? He'd have been supremely confident.
Even a fraudulently obtained physics doctorate surpassed 16th-century elementary students.
Truthfully, constructing the heptadecagon was something Cheng Jinzhou could undoubtedly complete within twenty minutes.
Researching its underlying principles could constitute a modern mathematics undergraduate thesis, but applying known methods? That was middle school material.
The problem was, to observers, Cheng Jinzhou didn't appear to possess era-transcending abilities.
And Dr. Cheng himself wasn't prepared to reveal such capabilities.
Time ticked by.
His opponent Cheng Jinhao hunched over the table early on, attempting an approximate heptadecagon. At fourteen, he clearly underestimated the challenge—this required two centuries of accumulated mathematical brilliance. Too many theorems and concepts needed prior development.
Knowing this, Cheng Jinzhou simply stood aside, watching the crowd with amusement.
The Cheng clan represented this world's most educated elite. Each had received nine years of compulsory education at their prestigious family school. Yet facing a problem two centuries ahead, they were no different from young Jinhao.
Most pointed between the two boys with knowing looks. Clearly, the child laboring at the table appeared more credible than the one who'd given up.
Cheng Jinzhou disliked the spectators' varied expressions.
Especially when the black-robed astrologers eyed him as a "lazy heir." That provoked outright fury.
As a former active doctoral candidate, he hated being seen as an unworthy scion—even if he had cheated repeatedly...
Without waiting for parental reactions, he impulsively confronted the astrologers: "Can any of you solve it?"
"Cheng Jinzhou!" His father's angry shout came first.
The black-robes lacked even one-star ratings, but as potential official astrologers, they commanded respect—certainly not to be challenged by a child.
Unfazed, the never-rational Cheng Jinzhou pointed at each in turn: "You've studied astrology for years. Can you answer this? What right have you to mock me?"
His tone was aggressive, but mathematically, he could indeed look down on the Cheng family's astrologers. He declared boldly: "This problem currently has no solution. Am I wrong?"
The scholarly challenge silenced the room. Seeing the matriarch remain quiet, Prefect Cheng also held his tongue.
The astrologer who'd posed the first question stroked his beard, unoffended: "I, Wu Zong, cannot solve this."
His dignified admission won immediate approval, sparking lively discussion—another dinner party topic secured.
Never one to back down, young Cheng Jinzhou pressed: "Master Wu, you haven't answered completely. Not just you—no astrologer can solve this, correct?"
"This..." Wu Zong tugged his beard, reluctant to admit the profession's limitations.
Perhaps because of his youth, the normally stern father didn't intervene, instead observing his son's performance. As prefect, he'd rarely spent time with his growing child and wanted to assess the sickly boy's knowledge and demeanor.
Cheng Jinzhou didn't press further, turning to the matriarch: "Grandmother, I know this problem is currently unsolvable, while Cheng Jinhao doesn't. Thus, though neither completed it, my understanding is superior, no?"
"Benevolent" Cheng Bingxun interjected smoothly: "Jinhao diligently attempted the task while you rely on trivial knowledge and cunning to steal victory. The loss is yours."
For a main branch heir to meddle in children's games was disgraceful enough. His blatant partisanship drew murmurs even from non-Long Branch members:
"Benevolent Cheng Bingxun... Miserly Cheng Bingxun... Incorruptible Cheng Bingxun..."
The litany of titles—many new to Cheng Jinzhou—nearly made him laugh aloud. Only thoughts of the coming-of-age gifts restrained him.
The matriarch ignored his argument, smiling serenely: "Since neither succeeded, and considering the earlier question, Jinzhou may proceed. He is, after all, the main heir."
That "main heir" comment made "Benevolent" Cheng's face flush.
Cheng Jinhao was also an heir, just from a distant branch. Without his father's interference, the matriarch wouldn't have emphasized lineage. Now father and son experienced the caste system's cruelty firsthand.
"Miserly" Cheng Bingxun could only watch helplessly as Cheng Jinzhou answered correctly and strode toward the exit, silently praying.
The minor incident became mere gossip for the Chengs, who soon dispersed—only households with children remained, hoping to partake in the coming-of-age ceremony's auspicious energy.
Cheng Jinzhou stepped confidently into the bright longhouse.