The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my exercise book of the ninth volume, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is the East-West City? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiaoying's, but xu teacher says their result is right. Why? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is: 45 × 2.5 = 1 12.5 (km),112.5+18 =18. But after careful consideration, I think something is wrong. In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the middle point of the east and west cities", but it does not mean that it has not yet reached the midpoint or has exceeded the midpoint. If it is not from the midpoint 18 km, the formula is the previous one. If the formula should be 45× 2.5 = 1 12.5 (km),112.5-18 = 94.5 (km), 94.5× 2 =1. 112.5+18 =130.5 (km), 130.5× 2 = 26 1 (km), 45× 2.5 =/kloc.

In daily study, there are often many answers to math problems, which are easily ignored in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy for us to ignore other answers and make the mistake of generalizing.

About "0"

0 can be said to be the earliest number that human beings have come into contact with. Our ancestors only knew nothing and existence at first, and none of them was 0, so 0 isn't it? I remember the primary school teacher once said, "Any number minus itself equals 0, and 0 means no quantity." This is obviously incorrect. As we all know, 0 degrees Celsius on the thermometer indicates the freezing point of water (that is, the temperature of ice-water mixture at standard atmospheric pressure), and 0 is the dividing point between the solid and liquid state of water. Moreover, in Chinese characters, 0 means more as zero, for example: 1). Decimal number. 2) the quantity is not enough to meet the demand of a certain unit ... At this point, we know that "no quantity is 0, but 0 not only means no quantity, but also means the difference between solid and liquid water, and so on."

"Any number divided by 0 is meaningless." This is a "conclusion" about 0 that teachers from primary school to middle school are still talking about. At that time, division (primary school) was to divide a copy into several parts and figure out how many there were in each part. A whole cannot be divided into 0 parts, which is "meaningless". Later, I learned that 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always smaller than any small one in the process of change) and it should be equal to infinity (the absolute value of a variable is always greater than any large positive number in the process of change). This leads to another theorem about 0: "A variable whose limit is zero is called infinitesimal". On the tiled floor or wall, adjacent tiles or tiles are evenly stuck together, and there is no gap on the whole floor or wall.

For example, a triangle is a plane figure composed of three line segments that are not on the same line. Through experiments and research, we know that the sum of the inner angles of a triangle is 180 degrees, and the sum of the outer angles is 360 degrees. The ground can be covered by six regular triangles.

Look at the regular quadrangle, which can be divided into two triangles. The sum of internal angles is 360 degrees, the degree of an internal angle is 90 degrees, and the sum of external angles is 360 degrees. The ground can be covered by four regular quadrangles.

What about regular pentagons? It can be divided into three triangles, the sum of internal angles is 540 degrees, the degree of one internal angle is 108 degrees, and the sum of external angles is 360 degrees. It cannot cover the ground.

Hexagon can be divided into four triangles, the sum of internal angles is 720 degrees, the degree of one internal angle is 120 degrees, and the sum of external angles is 360 degrees. The ground can cover three regular quadrangles.

A heptagon can be divided into five triangles with an inner angle of 900 degrees, an inner angle of 900/7 degrees and an outer angle of 360 degrees. It cannot cover the ground.

From this, we get that. N polygons can be divided into (n-2) triangles, the sum of internal angles is (n-2)* 180 degrees, the degree of an internal angle is (n-2)* 180÷2 degrees, and the sum of external angles is 360 degrees. If (n)

We can not only cover the ground with a regular polygon, but also cover the ground with two or three kinds of figures.

For example: regular triangle and square, regular triangle and hexagon, square and octagon, regular pentagon and octagon, regular triangle and square and hexagon. ...

In real life, we have seen all kinds of patterns composed of regular polygons. In fact, many patterns are often composed of irregular basic graphics.