It is easy to use the stacking technique to calculate the problem, and the next few questions are the problems that need to use the "Great Derivation Technique" and "Stacking Technique" algorithms. Pen "Fun" Pavilion www.biquge.info

These questions involve practical problems in engineering, military service, and military service, and cannot be answered without these algorithms.

At this time, most of the arithmetic questions were already the content of "Nine Chapters of the Book of Numbers" and "Sun Tzu's Arithmetic", which was one level deeper than "Nine Chapters of Arithmetic", and Huang Bowen even skipped two questions and waited for the time to be answered.

Just like this question, he said: "The Weiwei military camp is in the west of the town, and I don't know how many soldiers there are in the camp." Three thousand six hundred and forty bowls, see if you run out. Three people eat a bowl of rice, and four people eat a bowl of soup. May I ask the gentleman who knows how many soldiers there are in the battalion. ”

Although it is not very difficult, the time is limited, and he can't stay on each question for more time and solve the following first, after all, these problems are complicated and time-consuming.

Huang Bowen has passed the age of establishment, but he still has not married a wife, although his parents have hoped that he will study and make a name for himself since he was a child, but he has been a child for many years.

It is because he has been obsessed with arithmetic in the eyes of others since he was a child, and these eight articles are not done well, and the fame of natural talent cannot be tested.

And his father was originally a down-and-out showman, the family life was hard, barely enough for food and clothing, after the death of his parents, his life was even more poor, all by going south and north to sell some commercial goods to make a living, the hardships and hardships of life made him numb, but why didn't he have a dream in his heart?

Xuanfu Town recruited officials, and the focus on practical arithmetic gave him hope, and the opportunity was just around the corner. How can you not work hard?

He roasted his frozen hands on the stove beside the table, rubbed his face vigorously, and continued to concentrate on answering the following questions.

Then he was stunned for a moment and looked at the following question: "Metaphysical question? ”

Liu Dongyang, who was sitting in a few rows in front of him, also shrank his eyes: "Geometry questions? ”

Liu Dongyang's family background is happier than Huang Bowen's, after all, his parents are still alive, he also married a wife, and has a son and a daughter, which can be regarded as a happy life. The ancestors were even wider. So he can support him and win the show. also lived a rich and young life of clothes to stretch out his hands and food to open his mouth.

Liu Dongyang has received a good family education since he was a child, and he is also very interested in arithmetic, as early as a child. He found ancient mathematical masterpieces on his father's bookshelf. Nine Chapters of Arithmetic. Since then, I have been fascinated with mathematics.

Later, he collected a lot of arithmetic books, that is, Xu Guangqi's translation of Euclid's "Geometric Originals", which also collected.

The characteristics of Chinese and Western mathematics are their respective strengths. It was an eye-opener for Liu Dongyang.

Western studies pay attention to rigorous logic, clear reasoning, and advance layer by layer, and finally get the result. In middle school, the emphasis is on the solution method, pay attention to calculation skills, no matter what the process is, the result is a bit like the quality education of later generations, and Western learning is a bit like exam-oriented education.

However, their respective charms and the different mathematical ideas of the two sides still make Liu Dongyang lost in the ocean of mathematics. While studying the "Nine Chapters of Arithmetic", he also absorbed the new ideas of the "Geometric Original", which made his mathematical attainments more and more profound.

It's just that the good times didn't last long, Liu Dongyang's family fell into the middle, so he had to change careers to do business, and then earn some money to barely support his family, after all, good mathematics does not mean that business is strong.

When Xuanfu Town was recruiting officials, Liu Dongyang's family was studying business in Beijing, and the family only discussed it casually, so they resolutely came over to apply for a job.

In the "Geometry Original", Xu Guangqi determined that "metaphysics" is called geometry, and there are also translated names in it, such as "parallel lines", "triangles", "diagonals", "right angles", "acute angles", "obtuse angles", "similar" and other Chinese noun terms, all of which are familiar to later generations.

So as soon as he saw this topic, Liu Dongyang had a thought in his heart: "Geometry question ......"

Like Huang Bowen, he also skipped the question, in fact, not only Liu Dongyang and Huang Bowen, but also Li Tanran, Zhao Zhongju and others kept skipping the question.

They want to see if there are any questions they can do in the back, after all, it is different from yesterday's exam, and today's arithmetic questions are still traceable.

Seeing the geometry questions, everyone took out their own rectangles and compasses, and when they entered the examination room, the examiner also handed out pencils. That moment is also known as the curved ruler, carpenters are mostly using it, but to do arithmetic problems, the moment is naturally also needed, and there is a compass, which appeared as early as the Xia Dynasty.

Huang Bowen looked at this question carefully: "If you want to make a round city, you don't know the circumference, open the door on all sides, and there are cross avenues outside the door. Its northwest crossroads are designated as dry land, its northeast crossroads are designated as Gendi, its southeast crossroads are designated as Xundi, and its southwest crossroads are designated as Kundi. …… Or ask: A and B are both on dry land, and B is standing three hundred and twenty steps eastward. A walked 600 steps south and saw B, and asked how many miles is the path? ”

"To answer the question, you need to write the solution and play the grass."

Huang Bowen exhaled deeply: "I will respond with the circumcision technique!" ”

He drew a triangle on the draft with a rectangular object, and the three vertices were set as three points: heaven, earth, and stem, and then drew an inscribed circle with a compass to represent the round city, and he calculated: "The law of words and numbers comes from the circle, the circle comes from the square, the square comes from the moment, and the moment comes from the ninety-nine-eighty-one." Therefore, the moment is broken, and it is thought that the sentence is wide three, the stock repair is four, and the diameter corner is five ......"

He hooked three strands and four to make a diagram, set the center of the inscribed circle as the center, and intersected with the triangle and the inscribed circle from top to bottom at the three points of the sun, south and north respectively. From left to right, the horizontal line of the center intersects with the triangle and the inscribed circle at the three points of Sichuan, east and west, etc., respectively, and then finds the string.

Liu Dongyang also took a deep breath and began to draw a sketch: "Set up a right-angled triangle and divide it into three points: A, B, and C......"

Huang Bowen was playing loudly on the abacus: "Pythagorean seeks its strings, multiplies the strands, and doubles it as a result......"

Looking at the results on the abacus, he wrote down with satisfaction, at this time Liu Dongyang also used the Euclidean geometric formula to calculate the hook and the fereme, and then used the Pythagorean theorem to get the result, he wrote: "Answer: The city path is 240 steps. ”

Although the geometry question has been tested to the content of the "Zhou Ji Sutra" at this time, the first question is relatively simple, that is, Zhao Zhongju grinded and drew a map for a long time, and finally made it.

The following geometry questions are relatively simple, like this: "Today there is a bamboo one foot high." At the end of the fold to the ground, go to the three feet, ask the folder how high is it? ”

Huang Bowen and Liu Dongyang used Chinese and Western methods respectively, and they also calculated at the same time.

However, the following question is difficult, but it is connected to the round city above, but it says: "Or ask if there is a tree 480 steps south of the west gate, and 200 steps east of the north gate to see it, how many miles is the path?" ”

Huang Bowen rubbed his face vigorously for a while, and then used the Tianyuan technique: "I set Tianyuan one as the radius, and put the southbound step on the ground......"

He calculated: "Multiply two steps to be true." The two lines are step by step and follow. One step is a common method, and the radius is obtained. ”

Liu Dongyang also draws: "The remaining radius is unknown......"

Zhao Zhongju turned around and did it again, and Li Tanran finally figured out the problem of the chicken and caught up.

"Now there is a product and a multiplication. Debulation. The remainder is multiplied and summed. 170,162 steps. Only the cloud and the truth are good. The fourth is to benefit the party, the third is to be honest from the top, and the second is to benefit the lower incorruptible. One is the corner, three square open, such as a quarter of the flat. Q, long, flat geometry? ”

Huang Bowen replied: "12 steps flat, 30 steps long. ”

"Today, there are twenty-four steps of the yellow side multiplied by the straight product, only the cloud strand strings and nine steps, ask the geometry of the hook?"

Huang Bowen replied: "Three steps. ”

"Today, there are strands that are more powerful and more string-less than strands. Only the cloud hook power plus chord is more and the same as the hook multiplication chord. Q: Strand geometry? ”

Huang Bowen set Tianyuan one as a share, and Di Yuan one as a hook string, and finally replied: "Four steps." ”

He felt a dizziness in his head, and a throbbing pain in his temples. Liu Dongyang also put down the brush and closed his eyes slightly, but Huang Bowen shook his head and still looked at the next question: "Today, there are strands of strings that are more dividing the strings and the straight product." Only the cloud Pythagorean is more harmonious than the dividing string and the same as the hook. Ask chord geometry? ”

Huang Bowen tried his best to sit firmly, and exhaled slowly, he was deeply proud to be able to answer so many questions in the exam, but there was still the finale of the Marquis of Yongning behind him, and he must do it.

He picked up the moment and pencil and drew on the draft: "I set up the Tianyuan one as the hook, the earth yuan one as the share, the human yuan one as the string, and the object one as the open number!" ”

Finally, after he finished answering this question, he finally saw the finale set by Yongning Hou Wang Dou.

"The Jingbian Army has generals who are good at using guns, and some generals are good at using artillery, and the talented people are piled up with sun-shot geese, and the bigger the stack, the higher the accumulation, Xuan smiled and said: I bombarded it, and the Eryu piled up all the spans."

"When you know that the cones are piled up as a sharp cone, when you know that the cones have the principle of accumulation, the number of yuan starts from the silk hair and increases, and the stacking becomes a flat cone. A certain number of elements is stacked into a square, and the number of elements with less and more is stacked into a flat pyramid, and the square number starts from the silk hair and gradually increases and stacks it, then a sharp pyramid is formed. ”

"A certain square stack is a square, and a square stack with less upper and lower is a sharp cone. The number of cubes begins with the silk hair and gradually increases into a surface, and the stacked one becomes a three-fold cone. When you know that the bottom of the pyramid above the three times is square, only the upper four sides are not flat and concave, and the more you multiply, the more concave it is. ”

"When we know that the number of three-fold squares starts from the silk hair and gradually increases into a surface, and the stack becomes a four-fold sharp cone, from then on it progressively to infinity, and the line, surface, and body all have a circular principle."

"May I ask you, sir, what is this pyramid algorithm? How much does the cone accumulate? Xuan shelled it, how much is the product in this circle? ”

Huang Bowen was dumbfounded, his brain was buzzing, and he subconsciously thought: "I stand up to cut the circle, stack ......"

Then I was stunned, although the circumcision can be used to infinitely close to the area of the circle, it is said that the cutting is fine, and the loss is small, and the cutting is cut again, so that it cannot be cut, it is combined with the circle, and there is nothing to lose, but it is not enough to solve the problem at hand.

This problem has an infinitesimal division and an infinite sum, and then sets the setting, "when we know that all the vehicles have a sharp cone", "when we know that all the cones have the principle of accumulation", and then in the limit thought, the sharp cone seems to have curves and movements.

Zhao Xuan was also asked to shell the area of movement, and it seemed that there were mutual activities in between.

Because the cone is constantly getting bigger and smaller, the trajectory of the shell passes, and the area is not the same.

This, how is this producted?

All kinds of pictures were spinning in his head, and Huang Bowen sat dumbfounded, making the buzzing in his head even louder.

"Son, taking the test is the right way!"

Tears welled up in my mother's eyes.

"Wen'er, how can you go on like this?"

The father, who had always been strict, didn't say anything to him, just shook his head, a look of disappointment flashed in his eyes, and then turned around and walked away.

"Huang Bowen, have you been a child for decades?"

The contemptuous and ridiculous eyes of the classmates were so piercing, humiliating, blowing, and flashing from the past.

"No, I'm going to make this question and become famous all over the world in one fell swoop!"

Huang Bowen struggled, he reached out to take it to calculate, but a burst of Venus appeared in front of him, making him unstable. He tried his best to hold on to the table, his body was still shaking, and suddenly, a mouthful of blood spurted out, and the world was spinning in front of him, and he couldn't support it anymore, so he fell to the ground like that.

There was an exclamation in the examination room, and Zhao Zhongju shouted: "It's terrible, someone vomited blood in the exam......" (to be continued. )