Han Qian returned to the east courtyard and saw that there was a lamp in the hall, Zhao Ting'er was doing something at the desk, and Mrs. Xi was kneeling opposite the bookcase, helping Zhao Ting'er sort out the calculation draft, and when she saw Han Qian coming, she retreated far away.

Han Qian glanced at Mrs. Xi, and secretly felt that the time was not ripe enough, so he walked to Zhao Ting'er and sat down, looked at her sad face, took the calculation draft, and saw that Zhao Ting'er was actually calculating trigonometric functions.

To make a goniometer, it is also necessary to cooperate with the trigonometric function value to calculate the elevation difference.

Although trigonometry was only the content of elementary mathematics in later generations, trigonometry, which was based on the Pythagorean theorem, was mainly born from astronomical observation and calendar calculus, and all the relevant knowledge was fragmented and unsystematic.

Zhao Ting'er is smarter, but after all, it has not been a full year to study with him, and it is really difficult for her to use the unstructured knowledge of trigonometry to calculate the trigonometric function values independently.

The easiest way to determine the value of a trigonometric function is to calculate the value after the actual measurement is made by the plot, but no matter how accurate the plot is, the calculated value is biased.

However, it is actually a very large and difficult project to deduce all the trigonometric functions through purely mathematical calculations.

"Silly girl, I may not be able to deduce it." Han Qian knocked Zhao Ting'er with the calculation draft and asked her and Mrs. Xi to rest first.

In the dream, Zhai Xinping's level of physics and chemistry is not high, but financial analysis uses a lot of numerical calculations, and the foundation of mathematical calculus is not weak.

However, Han Qian did not remember the direct calculation method of trigonometric functions, and it was still extremely difficult to deduce it little by little with the help of the unstructured trigonometry principles that had been summarized by his predecessors.

Han Qian sat in front of the bookcase all night, the sky was bright, and he still had no clue.

This night, Zhao Ting'er and Mrs. Xi did not leave Han Qian to go back to the room to rest, and they were also accompanied in the hall.

Mrs. Xi fanned the wind with a fan, or helped repel mosquitoes; Zhao Ting'er forced himself to lie on the side of the case and watched Han Qian deduce various formulas, watching Han Qian finally crumple a large stack of calculations into a ball in a fit of anger, throw them into the waste paper box, and said with a smile: "It turns out that there are things that Gongzi doesn't know......"

Han Qian didn't want to spend his precious time in the vast mathematical deduction, thinking that it might take several generations to complete, and the sword hanging over their heads would be cut down in three or four years, and he really couldn't afford this time.

The next best thing is to draw as accurately as possible, and then actually measure the values of the corners and then calculate, so that you can make a rough table of trigonometric functions.

Han Qian vaguely remembered that the earliest trigonometric numerical table in later generations should have been formulated through this method.

Even if this table is used to measure and calculate the elevation difference, there will be an error of three to five meters, but in the implementation of large-scale water conservancy projects, it can still be corrected by other means of transportation.

Even if this wastes more manpower and material resources than expected, the technical level of the world is like this, and Han Qian alone can shake the sky.

Han Qian has taught Zhao Ting'er the method of drawing and calculation, and this thing also needs to have enough patience to do, so Han Qian pushed everything to Zhao Ting'er and Zhang Luo to do it with Mrs. Xi, and he called Qingyun to the back kitchen to find some food, and after eating a full meal, he went back to the bedroom to make up for sleep.

Han Qian slept until the afternoon before getting up, walked to the bedroom, and saw Zhao Ting'er lying directly on the bookcase and falling asleep, while Mrs. Xi was sitting curled up in front of the bookcase, turning out the manuscript he had thrown into the waste cardboard box in the morning.

Mrs. Xi was still wearing shackles, curled up on her side with her feet on the side, snow-white and delicate, except for the red marks on her ankles that were strangled by the shackles, there was no flaw.

Mrs. Xi was also quite alert, suddenly turned her head to look over, and then threw the calculation manuscript back into the waste carton with an expressionless face.

"You can't understand it," Han Qian said expressionlessly, "You go and bring me washing water first." ”

Listening to Han Qian's contemptuous and disdainful tone, Xi Ying was full of displeasure, but she had to admit that in her eyes, this pure mathematical deduction calculation manuscript was really like a book from heaven, and she didn't know how much more advanced than the arithmetic she learned when she was a child.

Han Qian smiled, thinking that a character like Hou Yang En of Liyang might be able to understand this calculation manuscript in the world, even if Mrs. Xi is the daughter of Gao Long, with a family history and a good education since childhood, but if she wants to reach the level of Hou Yang En of Liyang in arithmetic, the possibility is very small.

However, this can arouse Mrs. Xi's interest, which Han Qian is happy to see.

…………

…………

Although Han Qian has confirmed that the matter of directly calculating trigonometric function values cannot be done in a short period of time, if anyone is willing to study in depth in the future, this calculation draft should still be able to provide some help, and it cannot really be thrown into a waste carton and sent to the toilet to wipe the buttocks.

Han Qian sat down beside Zhao Ting'er, flattened the calculation draft, and recalled Mrs. Xi's confused and seductive demeanor when she looked at the calculation just now, as well as her snow-white jade feet, and secretly felt that it was no wonder that Feng Changyu knew that she might be a hidden danger, and finally couldn't help but take her into the room.

Zhao Ting'er's face is extremely beautiful, but her hands and feet are still a little rough, and her jade feet are not as attractive as Mrs. Xi's.

Han Qian sorted out the calculation draft, and took out the pattern drawn by Zhao Ting'er to measure - only if the drawing is accurate enough, the deviation can be reduced as much as possible when calculating the trigonometric function value.

It's a stupid way out of necessity.

There was a wire hammer for straighter on the bookcase, Zhao Ting'er was sleeping soundly, and inadvertently flicked his small hand out, the small cone copper hammer often rolled away on the side of the bookcase, Han Qian reached out and grabbed the end of the wire hammer, watched the cone copper hammer hang down and swing, and suddenly realized that the goniometer actually has a simpler way to build.

The land goniometer needs to ensure that the base is as horizontal as possible, but in addition to the spirit level, isn't the direction of the line hammer absolutely perpendicular to the horizontal plane at all times?

Isn't it much simpler and simpler to use a wire hammer to correct the levelness of the base?

He hadn't even thought of this before, Han Qian couldn't help but slap his face and scold himself for being such a fool.

Xi Ying brought the toiletry water, and saw Han Qian slapping his face while scolding himself for being a fool, and he didn't know what was going on with him.

After figuring out this truth, Han Qian went to redesign the goniometer and found that the goniometer could be designed very simply, and there was no need for a few craftsmen to do so many things with great fanfare.

Zhao Ting'er woke up sleepily, saw Han Qian rubbing his face in disgust, and asked, "What's wrong?" ”

"Look, a goniometer can actually be made like this!" Han Qian showed the artwork of the newly designed goniometer to Zhao Ting'er.

The newly designed goniometer only needs an upright rod, a half-disc with an angle tick and a line hammer, when actually measuring, the upright rod is inserted into the ground, and the line hammer is free to fall, at this time, as long as the center line of the semi-disc, that is, the zero degree angle, and the line hammer are kept coincidental.

In this way, the straight edge of the semi-disc is guaranteed to be in a horizontal position.

Then rotate the half-disc so that the two points of the straight line of the half-disc are kept in a straight line with the measurement target, and then directly read the angle between the half-disc and the line hammer, which is actually the elevation angle of the target they want to measure.

"It turns out that the truth is so simple!" Zhao Ting'er exclaimed happily, "Childe, you didn't expect that it would be stupid to let a craftsman use such a complicated method to build a goniometer!" ”

"You say I'm stupid again, try it?" Han Qian reached out and knocked Zhao Ting'er's head.

"I'm going to call someone now, and I'm going to inform the two craftsmen to make a goniometer according to the new method......" Zhao Ting'er jumped up happily to call someone.

Han Qian said: "Let them make a goniometer according to the stupid method, and the good method can't be taught to others, otherwise we won't be able to eat in the future." ”

Han Qian grabbed Zhao Ting'er and told her that the more complicated the goniometer used in Xuzhou is, when it is taken out for actual measurement, it can make the state capital appear tall and mysterious in the minds of ordinary people, making them know and be in awe.

In the current situation in Xuzhou, there are only benefits, not harms.

And the goniometer they built with the new method can be used to measure and calculate trigonometric function values.

To calculate the trigonometric value using the measurement method, to put it bluntly, is to draw the right triangle of the corresponding angle, measure the specific data of the three sides, and then perform a simple proportional calculation.

In this empirical way, when the accuracy of the scale is limited, only if the triangle is drawn large enough, the final trigonometric deviation can be small enough.

As long as Han Qian and the others build a simple version of the goniometer, they can use a straight wall as a straight edge of the triangle, and the vertical distance between the goniometer and the right angle as another straight line, and the hypotenuse can be simply calculated by the Pythagorean theorem.

In this way, the triangle they can use to calculate the trigonometric value can actually be more than ten meters in size, and the trigonometric value measured by this can naturally be controlled within a very small deviation.

And if each goniometer can correspond to a set of trigonometric value tables, then it can also eliminate the instrument errors of different goniometers.

Han Qian understands the truth of the three words "doing learning" more deeply, learning really has to be "done", if he hadn't started to do it in the past two days, he wouldn't have thought about it so carefully and deeply.

Seeing the happy appearance of Han Qian and Zhao Ting'er's master and maid, Xi Ying was puzzled in his heart, how could a person with such ruthless means have such unfathomable knowledge in his chest and abdomen.

When Tianyou's mother died of illness in the ninth year, Xi Ying was already fourteen years old, but even if she had studied arithmetic, she was quite shallow, and helped Zhao Ting'er draw in the morning, barely understanding the principle of measuring angles and using trigonometric function values to measure elevation, but there were still many doubts that she did not understand.

However, Han Qian was her brother-killing enemy, no matter how curious she was, she would not take the initiative to ask for advice.

At this time, Gao Shao came over with a stack of brochures, and when he saw Mrs. Xi present, he stood in front of the porch and did not rush in.

Han Qian beckoned Gao Shao to bring the booklet in.

These are all copies of the official letters and official letters that Wang Yu officially sent to Emperor Tianyou and the imperial court in the name of the state assassin history during the more than four years of Wang Yu's tenure as the assassin of Xuzhou, and the lord Bo Xue Ruogu has preserved them.

After Han Qian came back yesterday, he specially asked Gao Shao to go to Xue Guruo to get these copies, he wanted to see what Wang Yu had done in Xuzhou, and in the end he was not tolerated by the four surnames and Tanzhou.