"Don't you ever think it would be handy to find the length of the third side of a triangle if you already knew the other two?"
To explain the Theorem of Three Squares, Jin decided to start with its practical applications. He had a feeling that Kachea gravitated toward theories that had immediate utility.
"Hmm... Not really, no," she admitted.
Since she didn't have a personal example, Jin offered one of his own.
"For instance, say you're building a roof and you know the height and the width—or the depth. How would you determine the length of the rafters you need to lay diagonally?"
"I don't build houses, but I see your point. It would certainly be convenient if the length of a diagonal could be calculated like that."
"Right? The Theorem of Three Squares is a principle that applies to right-angled triangles. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides."
Written as a formula, it was $a^2 + b^2 = c^2$. It was a theorem typically taught to junior high school students in his old world.
"...Ah, so that's where square roots become useful?"
"Exactly."
Jin went on to explain that square roots often resulted in a long string of decimals and that calculating them manually was a chore, so people usually referred to a table instead.
＊ ＊ ＊
"Jin-dono, Kachea. Let's break for lunch."
The carriage came to a halt as a voice called out from the outside.
"Ah, is it noon already?"
Jin and Kachea stepped down from the carriage. They found themselves in a wide meadow overlooking a vast plain. A river of such scale it could only be described as "great" wound through the landscape.
"That's the Noshina River."
"I... see."
Once out of the carriage, Kachea reverted to her usual self.
Lunch was simple: hardbread soaked in meat soup.
"...Are you accustomed to such fare, Jin-dono?" Jed Alamold asked, watching Jin eat in silence.
"No, not particularly."
"I see..."
Jed had served this meal partly as a test. It was the kind of food a wealthy person would never willingly touch. While the hardbread softened when soaked, the soup was thin and lacked any real savory depth. Yet Jin finished his portion with a stoic expression, looking as though he didn't care about the quality at all.
(I understand him less and less.)
Between Lorenz's report, the information from Sergei, and the image of Jin he had formed with his own eyes, nothing seemed to fit together.
(If he is a magi, he should have lived a reasonably affluent life. According to my men, he is highly educated, so it's unlikely he's some commoner who just happened to find success. And yet, his behavior is entirely that of a commoner. I don't get it.)
＊ ＊ ＊
The carriage resumed its journey. Their next stop, Fan Village, was relatively close, and they arrived by 3:00 PM. Part of the reason for their swift progress was that the road followed a gentle downhill slope.
"So this is Fan Village."
"...I've been this far before," Kachea noted.
To Jin, the place didn't look much different from Taji Village. Kachea seemed to feel the same way.
"I think I prefer Taji Village," she remarked.
They stayed at the home of the village chief. Apparently, the detached wing was built large specifically to accommodate travelers like them. Jin and Kachea were each given a private room.
"The sun is still high," Jin noted.
It had only been thirty minutes since their arrival. He was considering taking a walk when Jed Alamold knocked on his door.
"Jin-dono, do you have a moment?"
"Yes, is something wrong?"
"It's nothing serious. A pump is broken here in Fan Village as well. If it's not too much trouble, would you mind repairing it? I'll pay the fee, of course... How does 1000 Toll sound?"
"Sure, I'll do it," Jin readily agreed.
"Much appreciated."
When Jin stepped outside with Jed, an elderly man was waiting. It was Lasnikov, the village chief. His hair was stark white, and his back had begun to stoop with age.
"I apologize for the trouble, sir," he said, bowing as he led Jin and Jed through the village.
"It's right here."
Located toward the back of the village was a suction pump of the same model Jin had seen in Taji Village.
"Ah, I can fix this in no time."
However, remembering Kachea’s repeated warnings about making repairs look too easy, Jin took his time with the work. He finished after about twenty minutes.
"All done."
He performed a test run to confirm water was flowing properly before reporting the completion.
"Oh! Oh, thank you so much!"
After being thanked profusely by the chief, Jin accepted the 1000 Toll from Jed Alamold and mentioned that he was going to walk around the village before returning.
"In that case, you should have someone guide you."
"I shall do it myself," the chief volunteered.
Jin grimaced almost imperceptibly but gave a small nod without a word.
"Over there is the communal laundry area."
"Do you use soap?" Jin asked.
"No, no, such things are far too expensive for us. We use Sapo fruit."
When shown the Sapo fruit, Jin noticed it looked very similar to the Rita fruit used in Kaina Village. He suspected they were closely related species.
"And that is the communal bathhouse."
"Does it use a hot spring?"
"What is a 'hot spring'? We use a magi-device to heat the water. The water itself is drawn up by a pump."
"This is the storehouse."
"A cold storage room, then."
"You are well-informed. We pack the winter snow in here, and it lasts until around autumn. We use it to keep perishable food from spoiling."
＊ ＊ ＊
Back in his room at the inn, Jin reflected on what he had seen.
From what he could tell, the cultural level here was similar to Ars, the world he had come from. However, magi-devices were disproportionately expensive. It was a puzzling discrepancy.
(Are there no engineers? Or did they all disappear?)
He dug deeper into the thought.
(If they are gone, why? And why are magi-crystals so costly?...Maybe I'll find the answers in Rofon.)
He had to get back to that world where Elsa was waiting for him. But for now, Jin was still wandering in the dark.