Urgent need for mathematical handwritten newspaper materials

Math newspaper needs you to write some math stories and some small problems!

For example, there is a legend that once, the mathematician O 'keeled taught a student to learn a theorem. After that, the young man asked O 'Keerid what benefits he could get from learning. O 'keeled once called a slave and said to him, "Give him three Apor, and he said he would benefit from what he learned." In ancient Greece, where mathematics was still very philosophical, it was understandable to be despised for exploring the origin of the world and the way of all things and what "benefits" to get. It's like another story: in a bar in Paris, a girl asked her lover why she was late. The young man said that he was working on a math problem. The girl shook her head and asked, "I really don't understand. What's the use of math when you spend so much time doing it?" The young man looked at her for a long time and then said, "Honey, what's the use of love?"

The scattered knowledge composed of experience is obviously less credible than the systematic knowledge, and we have always had more trust in the knowledge system. For example, Newton's mechanical system can accurately calculate the motion of objects, even if it is speculated that the solar eclipse in 1 million years is almost not bad; Darwin's theory of evolution, which takes species evolution and natural selection as the core, integrates the whole biological world into an orderly and organic system, making us know the relationship between different species.

However, even the classical knowledge system is not enough to carry all our trust all the time, because new experience and new research will adjust and update the old knowledge system, and new theories will replace the old ones. The appearance of Einstein's theory of relativity makes Newton's mechanical system a special case in a broader theory; With the development of genetic theory and the accumulation of fossil evidence, the idea of gradual change in Darwin's theory of evolution is challenged. Such cases are full of the whole history of scientific development. Let us look at those seemingly impeccable knowledge systems with suspicion from time to time and be wary of them.

However, when people pursue certainty and reliability, there is still an oasis of peace, that is, mathematics. Mathematics is our most reliable science, and once something is proved by mathematics, it is certain. In addition, the new mathematical theory opens up new fields, which can contain but not deny the existing theories. Mathematics is the only science in which the new theory does not overthrow the old theory, which is also a proof that mathematics is trustworthy.

Ultimate determination

What does mathematics pursue? We call Tessa Thales of ancient Greece the first person in ancient mathematics, because he didn't seek numerical solution for any regular object like the Egyptians or Babylonians, and his ambition was to reveal a series of truths. For example, for a circle, his answer is not about a special circle, but an arbitrary circle. He is interested in all the circles in the world. The ideal circle he created can be asserted: any straight line passing through the center of the circle divides the circle into two halves, and the truth he found reveals the nature of the circle.

mathematics requires universal certainty.

Mathematics should draw a clear line between results and proofs.

No matter how changeable the world is, we always have to rely on it. By pushing this reliance to the extreme, we can appreciate the power of mathematics. This is also the great use of mathematics.

Our ancestors began to use mathematics to solve specific engineering problems very early. In this respect, all ancient civilizations have excellent performances, but the ancient Greeks' understanding of mathematics deserves our admiration. First of all, the Pythagorean school, which regards numbers as the elements that make up the world, can be used to analyze the relationship of all things in the world, which is by no means comparable to our modern concept of "digital earth". It is a world outlook, and everything can eventually be reduced to numbers, and what is explained by mathematics can become a sacred belief. I think people who hold this idea must always be in awe of nature and will not be arbitrary and self-deceiving.

Secondly, the ancient Greeks used mathematics in debates. They demanded that mathematics provide arguments about political, legal and philosophical arguments, absolutely reliable evidence and "irrefutability"; They are not satisfied with empirical evidence (such as those of their predecessors in Egypt and Babylon), but further demand proof and universal certainty. What a lovely and solemn request! Those who have such requirements must be sensible and aboveboard.

In order to ensure the reliability of thoughts, thinkers in ancient Greece formulated the rules of thoughts. In human history, thoughts became the object of thoughts for the first time. These rules are called logic. For example, you can't admit a positive proposition and a counter-proposition at the same time, in other words, an argument and its counter-argument can't be true at the same time, that is, the law of contradiction; For example, a positive argument and a negative argument cannot be false at the same time, that is, law of excluded middle. All these efforts embody the pursuit of certain and reliable knowledge. A history of mathematics is the history of expanding the field of certainty.

1. The length, width and height of a rectangle are 8, 6 and 4 decimeters respectively. If you cut it into small cubes with an edge length of integral decimeters, how many cubes can you cut at least, and how many square decimeters does the surface area increase after cutting?

to cut the least, the side length of the cube should be the largest, and the greatest common divisor of 8, 6 and 4 is: 2, So the side length of a cube is: 2

then cut into: 8/2*6/2*4/2=24

The surface area of a cube is: 2*2*6=24 square centimeters

Then the surface areas of all cubes are: 24*24=576 square centimeters

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The original mass of salt is: 5 * 2% = 1g, and water is: 5+1-1 = 5g

Now the weight of brine is: 5/[1-37]. 5%] = 8g

That is, salt is needed: 8-(1+5) = 2g

I found this, and I hope it is satisfactory.