There are three difficult problems in ruler drawing in Euclidean geometry, which are said to have been "solved". However, there are still many people who continue to study these three geometric problems. Why? Are these people daydreaming? Don't! The so-called algebraic method is used to solve three major geometric problems. This "algebraic method" uses such a criterion, that is, "the number given by a known rational number after a finite number of addition, subtraction, multiplication and division." When explaining the possibility of "bisecting any angle", we can only use such a criterion as "the number given by the finite addition, subtraction, multiplication, division and square root of the known number". Comparing these two standards, the only difference between them is the word "rationality". If both criteria can be used in ruler drawing, then these two (double) criteria constitute a mathematical paradox, which impacts the foundation of mathematics, or this mathematical paradox tortures the certainty of mathematical foundation, which is a headache for the mathematical community. The paradox of mathematics gives the above-mentioned people the opportunity to continue to study the three difficult problems of geometry. This is a research group that can't disappear at present, and the number of this research group will only increase. Therefore, ruler drawing is a mathematical content with research value and prospect, and China people are also continuing to explore Euclidean geometry (or the "shape" part of mathematics) in their own way.

I hope Mr. Qiu Chengtong can see the above contents and guide middle school students correctly.

If there is some truth in the above, please publicize it among the students. Thank you.