Therefore, I believe that whenever the subject sees a very interesting topic, he will become very excited! Indeed, many high school mathematics are boring, at least in terms of topics. But these are very basic things, and there seems to be no better way to present them to everyone. But if this is all about mathematics, it is really wrong.
For example, let the subject draw a circle at random first, then find six points on the circle at random, mark them clockwise as A~F, and then connect AD AE BF BD CE CF with a straight line. Mark the intersection of AE BF, AD CF and BD CE as P Q R, then the subject will be pleasantly surprised to find that P Q R is actually in a straight line!
For another example, the subject will draw a circle, randomly find a chord AB, take the midpoint M of AB, and then take two chords CE DF. We connect C and F on the same side of AB, and the chords AB intersect with P Q respectively. Then the subject can intuitively see that M is just the midpoint of PQ! This beautiful theorem has a beautiful name called butterfly, which is said to be because it is painted like a butterfly. Please note that I didn't mean to belittle butterflies at all! )
The third example is like this: ask the landlord to draw two triangles abc and ABC on the paper, so that they just meet the requirement that the straight line Aa Bb Cc intersects at the same point. Then make the intersection of AB ab, PAAC AC and Q BC bc BC, and the intersection R of these three points also be on the same straight line.
Well, I admit that I won't draw a standard circle at will, so please use compasses and rulers wisely. )
I don't know what the subject thinks of these three examples, but at least it seems to me that this is a very strange thing. For example, in the first example, you just draw a few straight lines casually, and you will get a three-point * * * line information!
For another example, there can be violent views. Let the subjects open sharingan and treat this plane figure as a triangular pyramid, that is, the two triangles are different planes, and then the subjects can easily prove the conclusion. So when this triangular pyramid is pushed down ~ on paper, the conclusion is taken for granted!
Moreover, in the first two examples, if the circle is replaced by an ellipse, the conclusion is also valid. (Subjects will observe this when they tilt the paper with graphics at a certain angle in front of their eyes. )
These are obviously not coincidences! But what is hidden behind it?
For example, in the third example, there is a way to prove the situation of different planes first, and then transform the problem of two-dimensional planes into three-dimensional situations through a series of clever auxiliary lines! Don't you think it's incredible that a two-dimensional geometric proposition can be proved in a three-dimensional space? ! )
I don't know whether these three examples have aroused the interest of the subject, but I might as well assume that they have really aroused the appetite of the subject. This assumption is irrefutable. Then the subject can almost see that there are many wonderful phenomena in mathematics.
Even more strange is:
For every positive integer n, it can always be divided into some positive integers that will not exceed its own size, such as 4 =1+3 = 2+2 =1+1,so how many such splitting methods are there? Let p(n) be the number of all possible partitions. (We regard the split of 3 as the split of 1+2 is the same as that of 2+ 1) So far, nothing strange seems to have happened! But in fact, strange things have happened quietly. It can be proved that p(5n+4) is definitely divisible by 5. For example, p(4)=5, but actually 4 =1+1=1+1+2 =1+3 = 2+2 = 4.
Isn't that strange? What's more, p(7n+5) can definitely be divisible by 7, and p( 1 1n+6) can definitely be divisible by1. And only a and b can satisfy that p(an+b) is divisible by a! Zhang Liao's voice in the Three Kingdoms Killing: I didn't expect it! ! )
(In addition, kindly remind the subject not to try to count too many examples, because as long as n is slightly larger, p(n) will be particularly large! )
The math behind this example is very high. If the subject is interested, you can spend your time by yourself ~ ~ ~)
Mathematics is actually a field full of O'Henry's humor. Everything is so unexpected, but it is really reasonable. Forgive me if I can only give some elementary examples, but if the subject finally walks into the classroom of the university and chooses a math class to listen to for one semester, you will find that math is still very interesting!
Is math really annoying? In fact, it is really an introduction to middle school mathematics now, but it shows some not very interesting results!
Finally, I hope the subject can cheer up and get a satisfactory result in the college entrance examination! Come on ~ ~ ~
(P.S. Degang just said it was the hatred of eating fruit between peers! I didn't mean to lure the subject into the pit of mathematics at all. I just tried my best to describe a lovely picture. Although as far as my word control ability is concerned, I am likely to fail, but I still hope to arouse the subject's interest in mathematics, and finally I can naturally face the test paper in the college entrance examination and get a good result! That's all! But there are also very loving peers ~ ~)