Secondly, the right triangle is constructed by using the properties of geometric figures, and the distance from the point to the straight line is obtained by multiplying the bottom of the triangle area by the height.
Thirdly, the relationship between normal vectors, that is, the inner product formula of plane vectors, is used to represent the required straight line, and the curve is turned into a curve to achieve the purpose of finding the straight line.
The three methods introduced here have their own advantages and disadvantages, but they all lead to the same goal. Finally, the purpose of finding the distance from a point to a straight line can be achieved. Reflecting on their own performance in teaching, students still understand how to prove the truth with only one geometric figure, but how to find the distance from a special value to a general point is not only unknown to students, but also a little understood by me, because there is no actual process of deriving the formula, and students only know the formula. I don't know how to interpret and understand memory. From this point of view, many conclusions in mathematics textbooks omit the proof process, which makes me take it for granted that students can solve problems by using formulas without considering the proof process. It takes too long to finish the mathematical formula directly, and the effect is not good. Because of rote memorization and slight mistakes, the whole operation process is wrong and wastes energy.
The video of mathematics micro-course above onion mathematics showed me the ins and outs of various mathematical knowledge points, which inspired me to pay attention to the proof process of mathematical knowledge points and not just stay on the surface.
Take the general equation of a circle as an example. I just removed the brackets from the standard equation of the circle. As for what form can represent a circle, I directly tell the students the formula and give up letting them think about what can represent a circle and what can't. Students can't use all kinds of new questions flexibly by rote learning. For example, some math problems change the coefficient of quadratic term, which makes students very confused. How to bring them into formula judgment at this time? If students know in advance how to judge whether the general formula of a circle can represent a circle, they will actively try to give a formula to judge the value on the right. If the value is greater than zero, it can represent a circle, which is meaningful.
In the process of teaching math knowledge, if the math teacher doesn't do well, he is likely to finish some deformation problems of students, which will become the bottleneck to improve math performance.
The most impressive mathematical knowledge is the general equation of a straight line. Originally, I thought the so-called general equation of a straight line was a master, because the general equation of a straight line can represent all forms of a straight line. After reading onion mathematics, I know that the general equation of straight line has very profound geometric significance. The knowledge of mathematics is very simple, but behind it is the lifelong exploration and mathematical research of mathematicians.
As the successors of mathematics learning, we should inherit and understand the proofs and puzzles of our predecessors in this particular mathematical knowledge, break through the puzzles and have a deeper grasp of related mathematical problems. On this basis, students can be taught a correct attitude towards mathematics research, and students who grow up in this environment can become real contributors and researchers in the field of mathematics.
Pythagorean theorem has an enviable application in our life, and we should use it at any time. However, such problems have also puzzled the predecessors of mathematics for a long time. They overcame many difficulties to discover their relationship. Pythagorean theorem is only a special case of cosine theorem, and great mathematical research has promoted the progress of human history!