The main meaning of this passage is that Duke Zhou asked, "I heard that you are very proficient in mathematics. I want to ask a question. There is no ladder to go up in the sky and no ruler to measure on the ground. How do you get some measurement data about the height of the sky and the ground? "
Shang Gao said: "Numbers come from the understanding of figures of circles and squares." There is a principle: when the moment of a right triangle gets a right-angled side' hook' equal to 3 and the other right-angled side' chord' equal to 4, then its hypotenuse' chord' must be 5. "
This dialogue is the "tick three" in China's ancient books. Four shares? The earliest record of string five. In modern mathematical language, the sum of squares of the lengths of two right-angled sides is equal to the square of the length of the hypotenuse of any right-angled triangle. It can also be understood that the square subtraction of two long sides equals the square of the shortest side. Based on the above sources, Chinese scholars generally call this theorem "Pythagorean theorem" or "quotient height theorem".
Shang Gao did not answer the specific content of Pythagorean Theorem, but Chen Zi, the descendant of Duke Zhou, used his knowledge of the sun and the earth to measure the shadow of the sun through Pythagorean Theorem, thus determining the height of the sun. This is the scientific practice of ancient China people using Pythagorean theorem.
Chen Zi, the descendant of Duke Zhou, also became a mathematician. He described in detail the whole plan of measuring the height of the sun. This Chen Zi was an authority on mathematics at that time. Except for Shang Gao mentioned in the last section, the rest of Zhou Pian Shu Jing is all about Chen Zi.
According to Zhou Pian, Ji Jing, Chen Zi and others did use Pythagorean theorem as a tool to calculate the distance between the sun and Haojiang. In order to achieve this goal, he also used a series of other measurement methods.
Chen Zi used a hollow bamboo tube with a length of 8 feet and a diameter of 0. 1 foot to observe the sun, so that the sun just filled the round hole of the bamboo tube. At this time, the ratio of the diameter of the sun to its distance from the observer is exactly the ratio of the diameter and length of the bamboo tube, that is, 1:80.
After such measurement and calculation, Chen Zi and his research team measured that the sun was 60 kilometers below the sun and the sun was 80 kilometers above the sun. According to Pythagorean theorem, they got a Wan Li of 10.
This answer must be wrong now. But at that time, Chen Zi was full of confidence in his plan. He further elaborated on the plan.
At noon on summer solstice or winter solstice, an 8-foot-high pole is erected to measure the sun's shadow. According to the actual measurement, the sun shadow is 65,438+0.5 feet in the south and 65,438+0.7 feet in the north. This is the actual measurement, and the following is the reasoning.
The farther north, the longer the shadow. There is always a place where the shadow is exactly 6 feet long. In this way, the measuring rod is 8 feet high and the shadow is 6 feet long. The endpoint of the shadow to the endpoint of the measuring rod is exactly 10 foot, which is a perfect right triangle with three strands, four chords and five.
At this time, the sun and the ground are similar to a right triangle magnified several times. According to the data just measured, if the north-south movement is 1 km and the length of the shadow changes by 0. 1 ft, then the shadow measured 60 km south should be zero.
That is to say, from this measuring point to the "sunset" point, it is just below the sun, which is exactly 60 kilometers, so if the daily height is pushed to 80 kilometers, it will tilt to 10 Wan Li.
Next, Chen Zi talked about how high and big the sky is and how many degrees the sun runs every day. He has the answer there.
Chen Zi never thought all this was wrong. If he knew that the boundless earth under his feet was just a small globe, with the volume of11.3 million of the sun, just like a dust floating in the air, I really don't know what his expression would be.
In the last part of the book, Chen Zi points out that there are 265 days and 4 minutes in a year, 65,438+February, 65,438+7 minutes in September and 940 minutes in January 29. This understanding, from zero to all, is basically correct.
Now everyone knows that there are 365 days in a year, which doesn't seem like studying, but at that time, Chen Zi's study was not that simple, although he was not entirely right.