For many students, summer vacation is very interesting, and some students take math as a part of their summer vacation life. Let's take a look at the students' summer vacation life.

One of the manuscripts of summer vacation life mathematics: interesting mathematics. Today, I finished my math homework and read the Grand View Garden of Mathematics. Mathematical enlightenment? The king of ancient Greece asked Archimedes, a famous mathematician, for a shortcut to learning mathematics. Archimedes wrote down two numbers on the paper:11,100 1. ? 1 1 1 1? Show? Unique? ,? 100 1? Show? Is it consistent? . It means: there is no shortcut to learning, so you can only persevere.

I thought it was very interesting, so my mother and I found a few more figures like this:

? 23456789? Show? Lack of clothing and food (10)?

? 7086? Show? Fall apart?

? 2468 10? Show? Coincidence

? 999? Show? Get one out of a thousand things?

Math is really interesting. I like it more and more

Summer Life Math Manuscript II: Math Summer Homework At noon today, I was doing math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:

There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.

I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?

Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.

Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.

The final result is 374 cubic centimeters. My formula is: 209= 1 1? 19 19=2+ 17 1 1? 2? 17=374 (cubic centimeter)

Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.

I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.

Today, I saw such a problem in the training of Mathematics 1+2. In a cubic casting with a base area of 648 square centimeters, what is the area of the remaining three-dimensional figure if the largest cylinder is removed with the opposite sides as the base?

Seeing this topic, I was very confused and thought: just say a bottom area, how to do it? My mother sitting in the chair looked at it and laughed at me and said, well, they all say that the level is high, and you can't even solve this problem. ?

I know my mother used the goad method, in order to irritate my competitive spirit and let me finish this problem. In order to make my mother think that her provocation was successful, I crustily skin of head did it, but I couldn't figure it out. But I'm not discouraged. I persisted and finally succeeded.

According to the drawing (to be drawn), it can be found that when a cylinder is cut off, a hole with the same size as the original cylinder will come out. Although the volume of the hole is the same as that of the cylinder, their surface areas are not the same, but the areas of the two bottoms are smaller than that of the original cylinder.

Therefore, the remaining graphic area should be equal to the area of the six faces of the cube minus the two bottom faces of the cylinder+the side faces of the cylinder.

The formula is 628? 6-628? 3. 14? 4? 2+628? 3. 14

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