Han Qian returned to the east courtyard and saw that there was a lamp in the hall and Zhao Ting'er was working on something at the desk. Mrs. Xi was kneeling on the opposite side of the desk, helping Zhao Ting'er sort out the calculations. When she saw Han Qian coming over, she stepped aside.
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Han Qian glanced at Mrs. Xi and felt that the time was not ripe yet, so he walked to Zhao Ting'er and sat down. Looking at her sad face, he took the calculation manuscript and saw that Zhao Ting'er was actually calculating trigonometric functions.
To make a goniometer, you also need to match the trigonometric function values to calculate the elevation difference.
Although trigonometric functions were only the content of elementary mathematics in later generations, the current trigonometry based on the Pythagorean theorem was mainly derived from astronomical observations and calendar calculations, and all relevant knowledge was fragmented and unsystematic.
No matter how smart Zhao Ting'er is, she has only been studying with him for less than a year. It is really difficult for her to use her incomplete trigonometry knowledge to independently calculate the values of trigonometric functions.
The simplest way to determine the value of a trigonometric function is to draw and make actual measurements before calculating the value. However, no matter how accurate the drawing is, the calculated value will be biased.
However, trying to calculate the values of trigonometric functions purely through mathematical calculations is actually a very large and difficult project.
"Silly girl, I may not even be able to calculate it." Han Qian knocked Zhao Ting'er with the calculation script and asked her and Mrs. Xi to rest first.
The person in the dream, Zhai Xinping, is not very good at physics and chemistry, but financial analysis requires a lot of numerical calculations, and his foundation in mathematical calculations is not weak.
However, Han Qian did not remember the direct calculation method of trigonometric function values. It was still extremely difficult to deduce it bit by bit with the help of the unsystematic principles of trigonometry that had been summarized by predecessors.
Han Qian sat in front of the desk all night, and it was bright and clear, but he still had no clue.
That night, Zhao Ting'er and Mrs. Xi did not leave Han Qian behind to go back to his room to rest, but also stayed with him in the hall.
Mrs. Xi fanned herself with a fan or helped to drive away mosquitoes; Zhao Ting'er leaned on the desk and watched Han Qian deduce various formulas, and finally watched Han Qian angrily crumple a large stack of calculations into a ball and throw it on the wastebasket.
He went into the cardboard box and said with a smile: "It turns out there are things that the young master doesn't know..."
Han Qian didn't want to waste his precious time on the vast mathematical deductions. He thought that it might take several generations to complete the work, and the sharp sword hanging above their heads would fall down in three or four years.
He really couldn't afford to waste 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 them. You can make a rough table of trigonometric function values first.
Han Qian vaguely remembered that the earliest numerical table of trigonometric functions in later generations should have been formulated through this method.
Even if you use this table to measure and calculate the elevation difference, there will be an error of three to five meters, but in the implementation of larger-scale water conservancy projects, you can still make corrections through other means of transmission.
Even though this would be a waste of more manpower and material resources than expected, the current level of technology is such that Han Qian alone cannot conquer the world.
Han Qian had taught Zhao Ting'er how to draw and calculate, and he also needed to have enough patience to do it. Han Qian pushed everything to Zhao Ting'er and asked Mrs. Xi to do it together. He called Qingyun to the kitchen to help.
I found some food, had a full meal, and then went back to the bedroom to catch up on my sleep.
Han Qian didn't get up until noon. He walked to the bedroom and saw Zhao Ting'er lying on the desk and sleeping soundly. Mrs. Xi was curled up in front of the desk, flipping through the calculations he had thrown into the waste paper box in the morning.
Mrs. Xi was still wearing shackles, her feet were curled up on one side, and they were white and delicate. Except for the red marks on her ankles where the shackles had been placed, there were no flaws at all.
Mrs. Xi was also quite alert. She suddenly turned her head and looked over, then threw the calculation manuscript into the waste paper box again with an expressionless face.
"You can't understand," Han Qian said expressionlessly, "Go and bring me some water first."
Hearing Han Qian's disdainful tone, Xi Rong felt unhappy, but she had to admit that in her eyes, this purely mathematical calculation script was like a heavenly book. It was much better than the arithmetic she had learned when she was young.
How much more advanced and profound is it?
Han Qian smiled and thought that only a person like Yang En, Marquis of Liyang, could understand this calculation. Even though Mrs. Xi was the daughter of Gao Long, she had a good family background and received a good education since she was a child, but she wanted to be good at arithmetic.
The possibility of reaching the level of Liyang Hou Yangen is slim.
However, Han Qian was happy to arouse Mrs. Xi's interest in this way.
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Although Han Qian has confirmed that directly calculating the values of trigonometric functions cannot be done in a short time, if anyone is willing to study in depth in the future, this calculation manuscript should still be able to provide some help, and it cannot be thrown into the trash as a scrap manuscript.
Cartons are sent to the toilet for wiping buttocks.
Han Qian sat next to Zhao Ting'er, spread out the calculation manuscript and put it in order. He recalled Mrs. Xi's confused and seductive expression when she was looking at the calculation manuscript just now, as well as her pair of snow-white feet. He secretly felt that it was no wonder that Feng Changyuming knew about her.
Maybe it was a hidden danger, but in the end I couldn't help but bring her into the room.
Zhao Ting'er has a very beautiful face, but her hands and feet are still a little rough, and her feet are not as attractive as Mrs. Xi. Thinking of this, Han Qian regrets that he could not create such interesting things as silk stockings in this world.
Han Qian organized the calculations and took out the drawings drawn by Zhao Ting'er to measure them - only when the drawings are accurate enough can the deviation be reduced as much as possible when calculating the values of trigonometric functions.
This is a stupid and helpless way.
There was a hammer for straight threads placed on the desk. Zhao Ting'er was sleeping soundly when he accidentally moved his little hand out. The small conical copper hammer rolled to the side of the desk. Han Qian reached out and grabbed the end of the thread hammer.
, watching the conical copper hammer hanging down and swinging, I suddenly realized that there is actually a simpler way to make the goniometer.
Land-based goniometers need to ensure that the base is as level as possible, but in addition to the spirit level, doesn’t the direction of the line hammer remain absolutely perpendicular to the horizontal plane at all times?
Then using a line hammer to correct the level of the base is simpler and much simpler than using a spirit level?
He hadn't thought of this before, so Han Qian couldn't help but slap himself in the face, scolding himself for being such a fool.
Xi Rong brought the wash water and saw Han Qian slapping her face and calling herself a fool, but she didn't know what was going on with him.
After figuring this out, Han Qian went to redesign the goniometer and found that the goniometer could be designed to be very simple, without the need for a few craftsmen to do so many things in a big way.
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 built like this!" Han Qian showed the drawing of the newly designed goniometer to Zhao Ting'er.
The newly designed goniometer only requires an upright rod, a semi-disc with angle markings and a line hammer. When actually measuring, insert the upright rod into the ground and let the line hammer fall freely. At this time, you only need to use the half-disk.
The center line of the disc, which is the zero-degree angle, just needs to coincide with the line hammer.
In this way, the straight edge of the semicircle is guaranteed to be in a horizontal position.
Then rotate the semi-circle so that the two straight points of the semi-circle are in a straight line with the measurement target. At this time, the angle between the semi-circle and the line hammer is directly read, which is actually the target elevation angle they want to measure.
"It turns out that the truth is explained clearly, it's really that simple!" Zhao Ting'er exclaimed happily, "Sir, you didn't think of it before, and you asked the craftsmen to use such a complicated method to build the goniometer. How stupid!"
"You tell me I'm stupid again, why don't you give it a try?" Han Qian reached out and hit Zhao Ting'er on the head.
"I'm going to call someone now to inform the two craftsmen to make a goniometer according to the new method..." Zhao Ting'er jumped up happily and went to call someone.
Han Qian said: "Let them build a goniometer using a stupid method. We cannot teach others all the good methods, otherwise we will not be able to make a living in the future."
Han Qian grabbed Zhao Ting'er and told her that the more complex the goniometer used in Xuzhou was, the more complex it would be when it was taken out for actual measurement, it would make the state appear taller, more mysterious and awe-inspiring in the eyes of ordinary people.
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Under the current situation in Syria, this has only advantages and no disadvantages.
The goniometer they built using the new method can be used to measure and calculate trigonometric function values.
Calculating trigonometric function values using the measurement method simply means drawing a right triangle with corresponding angles, measuring the specific data of the three sides, and then performing a simple ratio calculation.
With this empirical method, in today's world where the accuracy of measuring rulers is limited, only if the triangle is drawn large enough can the final deviation of the trigonometric function 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 side of the triangle, the vertical distance between the goniometer and the right angle as another straight line, and the hypotenuse can be hooked.
The stock theorem is simply calculated.
In this way, the triangle they can use to calculate the trigonometric function value can actually be more than ten meters in size. The trigonometric function value measured by this method can naturally be controlled within a very small deviation.
And if each goniometer can correspond to a set of trigonometric function value tables, then the instrument errors of different goniometers can be eliminated.
Han Qian has a deeper understanding of the meaning of "doing knowledge". Learning really has to be "doed". If he hadn't started doing it in the past two days, he would not have been able to think about it in such detail and depth.
Seeing the happy expressions of Han Qian and Zhao Ting'er, the master and maid, Xi Rong was puzzled. How could a person with such ruthless methods have such profound knowledge in his chest and abdomen.
When her mother died of illness in the ninth year of Tianyou's reign, Xi Rong was already fourteen years old. However, even if she had studied arithmetic, it was quite rudimentary. She helped Zhao Ting'er draw in the morning and barely understood the principles of measuring angles and using trigonometric function values to measure elevation, but she still
There are a lot of doubts that are not clear.
However, Han Qian was her brother-killer and 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 in his hands. Seeing Mrs. Xi's presence, he stood still in front of the corridor and did not rush in.
Han Qian waved to Gao Shao to bring in the booklet.
These are copies of memorials and official letters that Wang Yu formally sent to Emperor Tianyou and other ministries and departments in the imperial court in the name of the governor of Xuzhou for more than four years when he served as governor of Xuzhou. They are all preserved by the owner, Bo Xue Ruogu.
After Han Qian came back yesterday, he specifically asked Gao Shao to go find Xue Guyuo to get copies of these memorials. 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.
