Wanderer of the whirling world

Chapter 130 Another Calculation Problem

Jia Zhiqing saw that Xin Ziqiu didn't answer her own words immediately, but looked up at the sky, her eyes were shining with tears, she was surprised and thought to herself:
"Xiao Qiu, what does this mean? Could it be that he also encountered a trial similar to mine?"

Thinking that she almost fell in the last test just now, Jia Zhiqing couldn't help but her face was covered with red clouds, she quickly shook her head, put aside distracting thoughts, and said:

"If you don't want to say it, let it be."

When Xin Ziqiu heard the voice, he came back to his senses and said:

"Oh, it's really nothing, it's just that I met my dead father in the previous level, and I was a little bit sentimental."

After hearing this, Jia Zhiqing finally understood why Xin Ziqiu had that expression just now.

Thinking of his miserable life experience, there must be unspeakable difficulties, and he said apologetically in his heart:
"I'm sorry Xiaoqiu, I didn't mean to ask about your sadness."

Xin Ziqiu shrugged, smiled slightly, swept away the haze on his face, and said:
"It doesn't matter, it all happened a long time ago. Sister Zhiqing, how are you doing? What kind of test did you encounter?"

Jia Zhiqing blushed, shook her head and said:
"No...it's nothing. Just now, the Daluo Talisman appeared and protected my soul, so I passed...very smoothly."

When she said this, she lowered her gaze, counting the stones on the ground, not daring to look at Xin Ziqiu.

In fact, Jia Zhiqing had just met Xin Ziqiu in the form of a mirage in the final test, and she almost lost her mind. If the big Luo symbol on her body hadn't turned into a golden light and pierced the illusion, she might have failed immediately.

She has ghosts in her heart, so she is very shy when facing Xin Ziqiu.

However, when he heard that the test he encountered was not his own, he felt a little regretful.

The two of them were thinking about their own thoughts, when someone passed the test one after another.

First Taoist Xuancheng came out. He was not too surprised to see Xin Ziqiu and Jia Zhiqing, but he couldn't help being a little surprised when he found that the bureaucratic Taiwei Hong had passed the test.

Then there is the eminent monk who has become a monk, Baosong Arhat Ouyang Chun, he is profound in Buddhism, and his mind is like calm water, but nothing can seduce him.

Then came Jia Xian and several elderly scholars. These people have been studying all their lives, and they are mature, and they all passed the test one by one. With the red light on their foreheads, they came out one by one.

Finally, there are the brothers Zhan Zhao and Xiao Wuyi, martial arts masters with a firm mind, they have been resisting inner demons during their practice, and it is difficult to be tempted by foreign things.

Xin Ziqiu was relieved to see everyone appearing out of thin air.

This one doesn't seem too difficult.

But he suddenly remembered something again, and felt very strange.

In the past, he was also pulled into the inner scenes of Zixu Daoist and Taoist Xuancheng, but only the soul entered and the physical body was outside, but this mirage's inner scene seems to be able to include the human body as well.

Is it because the Taoism of the ancient magicians is different, or is there something else inside?
Another half an hour later, seven or eight losers were also sent out one by one.

Surprisingly, neither Zhong Xiong nor Jiang Ping passed this level.

Jiang Ping looked a little sad, sighed and said:
"This ghostly place is really evil. I saw Lao Wu. He said that he has a good life down there, and has been waiting for us old brothers to go there to get together."

Everyone sighed when they heard that his obsession was the dead Chinchilla Bai Yutang.

Back then, Bai Yutang died in the battle against King Xiangyang in the copper grid formation on the Sky Tower, which was an irreparable wound in Da Wuyi's heart. Otherwise, with Jiang Ping's ingenuity, he would never have been trapped by this small trial .

As for Zhong Xiong, there is no need to ask too much, this fellow is born lustful, so it is naturally a hero who is sad for a beauty.

It's just that he didn't aim at the treasure, but only hoped to build a relationship with Hong Taiwei and have a lot of backers, so he was not depressed, but laughed at himself.

Seeing that most of the people in the team have successfully passed the first test, Taiwei Hong nodded with satisfaction and said:
"It seems that you are all determined people. This ancient tomb of Lord Xinling is really extraordinary. If you want to get the treasure, there are still many hurdles. I hope you will continue to work hard and not let down the trust of the officials."

Everyone even claimed yes, without taking a rest, they walked through the bamboo forest and continued to move forward.

……

After walking about a mile or two, everyone suddenly heard the sound of rumbling torrents, and they were startled, not knowing what kind of raging waves were ahead.

Going forward for a while, I saw a towering cliff in front of me, with a huge waterfall on it, constantly impacting on the rocks, and finally pouring into a deep blue pool.

Under the sunshine, this big waterfall hangs upside down like a jade dragon, like a nine-day Milky Way, and it looks extremely magnificent amidst the green and green peaks.

At the place where the waterfall pours into, the pond water is tumbling, the water vapor is pervasive, and amidst the transpiring haze, a long rainbow appears faintly, crossing the sky, gorgeous and incomparable.

At this time, the sun was slanting to the west, reflected in the dense fog, appearing purple, adding a mysterious color to the spectacle in front of you.

Looking at the big waterfall, Xin Ziqiu couldn't help cheering secretly, thinking:
"It's no wonder that Li Bai said that 'the sun shines on the censer to produce purple smoke'. When the sun shines, the waterfall will indeed be filled with purple smoke. The ancients are not deceived."

He looked around again, and saw many exotic flowers and plants growing on the side of the pool, colorful, swaying in the water vapor, embellishing the beautiful scenery.

Among the flowers, there seems to be something buried.

Xin Ziqiu was about to step forward to see what happened, when Taiwei Hong stroked his hands and praised:

"Good water, good water! Let's take a rest here after walking for half a day."

Just as everyone was about to sit down, Xin Ziqiu had already seen the buried things clearly, stepped up and said:
"Look, my lord, there is another stone tablet here."

Hong Taiwei looked up in the direction of Xin Ziqiu's finger, and sure enough, there was a three-foot-high stone tablet hidden under the cover of vegetation, but it was surrounded by flowers and vines for a long time. plant.

He hurriedly found someone to clean up the stele, only to see that there were obviously more weird characters on it this time.

Lu Hanlin stepped forward, stared at the faint old eyes carefully for a long time, and then said:

"Report to Master Taiwei, this is the test of the second level, and the real level is said to be behind this waterfall."

Hong Taiwei looked around, and sure enough, on the side of the deep pool, there was a gleaming iron bridge that went straight into the waterfall.

He snorted coldly:
"Hmph, playing tricks, everyone, come with me, let's find out."

As he spoke, he took the lead and walked to the bridge.

This is a pain for a group of elderly pedants. They are usually pampered, and they have to be careful not to fall when walking on flat ground. Now they are on the wet iron bridge, and their feet are slipping. Sweating profusely, scratching ears and cheeks.

All the knights in Kaifeng Mansion had no choice but to support the civil servants one by one. Even Xin Ziqiu, because he was young and strong, had to help Lu Hanlin to cross the bridge together.

At the entrance of the waterfall, everyone was drenched in water again. Fortunately, the valley is like spring all the year round, so it is not too cold.

After the big waterfall, there is no water or waves, only a big grotto.

Warm hot air continuously spewed out from inside, drying everyone's clothes in a short while. It was indescribably comfortable in this humid place.

Everyone walked a little further in, only to feel that the cave is smooth and flat everywhere. The cave is actually carved by hand. I don't know what kind of person it is, who spent such a lot of money to build another cave after the waterfall.

There is no light source in the grotto, it should be a dark hole, but the more people walk forward, the brighter it is inside.

After a few feet, everyone discovered that the stone wall above the head in front of them had been replaced with a large piece of transparent crystal with a radius of several feet, and the sunlight penetrated through it, illuminating the grotto.

Not only that, but through the crystal, everyone could see fishes and shrimps swimming above their heads, and only then did they realize that they were at the bottom of the water, and they couldn't help but be dumbfounded.

Leading the lake water into the cliff, and then paving the road with crystals under it, whether it is conceived or actually implemented, I am afraid it will be difficult to reach the sky.

Even the royal gardens do not have such fantastic ideas and huge projects.

Xin Ziqiu used to go to the aquarium quite often, and he wasn't as surprised as the others, but he had to admire the skills of Fang Warlocks, thinking that even a fairy would have to spend a lot of effort to do this.

At this moment, there was no road ahead, only a stone gate lay across here, blocking everyone.

Hong Taiwei walked in front and pushed the stone door with his hand, but he didn't move a muscle.

Looking at the door again, I saw an irregular triangle drawn on it, and there were two square holes below. ten.

On the top of the triangle, there is a paragraph written in incomprehensible characters.

After translating it, it turned out to be another calculation problem.

"Ask a section of Shatian. There are three obliques, ten minor obliques, seventeen middle obliques, and twenty-one major obliques. Do you want to know the geometry of Tian?"

In modern terms, this question is to find the area of ​​the three sides of a given triangle.

After listening to Lu Hanlin's translation of the topic, Hong Taiwei turned around and smiled at the people behind him:

"Everyone, raise soldiers for thousands of days, now it's time to use you, please don't let me down."

As his words fell, several officials from the Imperial Academy and Sitianjian walked out of the crowd, and they came to the side of the stone gate, carefully watching the triangle.

Jia Xian's grandfather and grandson also came to the front and looked at it attentively.

Not long after, an old man with a gray beard said:
"Report to your lord Taiwei, the next officer will see that if you want to pass through the stone gate, you must first solve this problem, and then insert the corresponding answer cubes into the two square holes to open the mechanism."

Taiwei Hong saw that the speaker was Zhang Yun, the director of the Sitianjian, nodded his head and said:
"This official can also see it, do you have a technique to solve it?"

Zhang Yun and the others exchanged glances, and then said:

"Uh, this one can be used as a method of replenishing deficiency, but it is not easy to calculate accurately."

Hong Taiwei looked at him and said:
"Do your best."

As he spoke, he looked around and saw Xin Ziqiu holding his shoulders and tilting his head, as if he was thinking, so he asked:
"Captain Xin, do you have a good idea?"

Xin Ziqiu was taken aback, a little strange, so many scholars and great Confucians are here, why do you ask me?
He smiled and said:

"Report to Taiwei, I am thinking about it."

Of course, this kind of question obviously couldn't help him, but he also wanted to see how the ancients thought about the problem of geometric measurement, so he didn't rush forward to answer it.

The method of calculating the area of ​​geometric figures played an extremely important role in ancient times, because it involved land measurement, engineering calculations, etc., and had practical applications in real production and life.

Many mathematicians have studied the area formulas of various figures.

As early as the ancient Greek period, Hero of Alexandria gave the method of using the area of ​​the triangular sphere of any triangle in his works, which is called Hero's formula (also known as Helen's formula) in later generations.

It is a pity that Chinese mathematicians are lagging behind on this point. It was not until more than 1000 years later in the Southern Song Dynasty that the famous mathematician Qin Jiushao gave a similar solution to the "three oblique product" problem in "Nine Chapters of the Book of Numbers". method.

Therefore, some Chinese scholars also refer to Hero's formula as Qin Jiushao's formula.

However, like other ancient Chinese almanacs, Qin Jiushao did not prove the formula, and how he obtained this solution is unknown to future generations.

Before him, most of the methods of calculating the area followed the method of "supplementing deficiency with surplus" proposed by Liu Hui, a mathematician in the Three Kingdoms period, or the method of "complementing in and out". Graph Solving of Rules.

When measuring land, this method is a bit troublesome.

However, Qin Jiushao's method saves a lot of time, no complicated cutting is needed, and the area can be calculated by measuring the distance between two points.

Even for any polygon, it can be cut into triangles one by one, the areas are calculated separately, and then added.

Therefore, it can be said that this formula has greatly promoted the development of later generations of engineering.

……

But now, Qin Jiushao has not yet been born, and his three-oblique quadrature method has not been discovered, and all the masters who have intensively studied arithmetic can only rub the figure on the stone gate on paper, and carve it with a knife. To cut and mend.

But this triangle is not very regular, no matter how it is cut, it is difficult to make it into a square to solve it.

And if the cutting is too small, it is inevitable that the error will become larger, and it is difficult to obtain accuracy.

Everyone was busy for a long time, their foreheads were sweating, and they changed several sheets of paper for rubbing, but they couldn't find the right way.

Hong Taiwei was a little impatient seeing these people busy, looked at Xin Ziqiu again and said:
"Lieutenant Xin, seeing that you are calm and composed, I must have an answer."

Xin Ziqiu became more and more strange, thinking that even if I have solved the calculation problem of opening the treasure, you don't have to have so much confidence in me.

However, he also watched for a long time, and seeing the messy behavior of the people, he couldn't help but feel emotional. The number theory and algebra in ancient China are indeed at the forefront of the world, but geometry has no systematic development. It depends entirely on experience. When I return from the treasure, I have to write a basic geometry book.

But right now, he didn't intend to wait any longer, but wanted to teach everyone a lesson in geometry, so he stepped forward and said with a smile:
"I already have the answer below."

……

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　　It's time for the popular science of mathematics that we love to hear and hear. This time it's not number theory, but geometry.

　　
　
(End of this chapter)