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What was the earliest painting tool?
We often say that there is no Fiona Fang without rules, and "rules" and "moments" are tools for drawing circles and squares respectively. They are the earliest geometric drawing tools. Specifically, "gauge" is a compass that draws a circle; Moment is a rectangular ruler with scales on it. As early as in Oracle Bone Inscriptions, the word "rules and regulations" has been used. The word "gauge" is the shape of the planning circle, and the word "moment" is written. Many masonry portraits in Han Dynasty are painted with images of Fuxi and Nu Wa, from which we can see the basic forms of ancient rules and regulations. Sima Qian's Historical Records in the Western Han Dynasty recorded Yu Xia's "left is right" in water conservancy, which reflected the importance attached to ruler, moment, mark and rope as measuring and drawing tools in water conservancy construction.

In the related records of "rule" and "moment", the most important proposition is Pythagorean theorem. Pythagorean theorem is one of the most important discoveries in China's early mathematical history. It is recorded in the Book of Balance Calculation of Zhou Dynasty that when Zhou Gong and Shang Gao discussed astronomy in the early years of Western Zhou Dynasty, they mentioned "moment folding, which means that the three sides of Pythagoras are 3: 4: 5", which is a special form of Pythagoras theorem. In addition, the book also mentioned the property that "the moment of a ring is a circle". The Book of Zhou Kuai Shu Jing was written in the first century BC, that is, even later. Therefore, some people doubt the reliability of the question and answer between Duke Zhou and Shang Gao recorded in the book. Of course, about the age of Pythagorean theorem. Need more evidence. However, in connection with the complexity of ancient water conservancy construction projects in China and the required measurement knowledge, China has long discovered the general Pythagorean theorem, which is beyond doubt.

Gauges can be circles and arcs, and moments can be straight lines and right angles. According to Zhou Xie, the usage of moment in measurement is "using different pendulum methods of moment, according to the proportional relationship between the corresponding sides of hook, the horizontal and vertical directions can be determined to measure the height, depth and distance of distant objects".