No problem.

If you can't understand something at once, you can read it later.

Ⅱ Aha! What are the main contents of a brainwave?

Aha! A brainwave: When it comes to intelligence, it is difficult for us to bypass martin gardner, a world-famous popular science writer. He is open-minded and has strange ideas. Many difficult problems that require complicated calculations and great pains can be made smooth and simple by his mathematical and logical tools. He spared no effort to publicize mathematical science all his life, from topology and group theory to arithmetic and algebra, and absorbed countless people into the temple of mathematical science. His achievements are indelible.

Martin gardner is very knowledgeable, "aha! The book "A brainwave" is rich in content, from the simplest arithmetic and algebra to unfathomable topology and super-difference, covering a wide range and attracting attention with many "hot spots". Every reader can "get what he needs" and find interesting chapters suitable for his education level. The contents of this book can be divided into six categories: combination, geometry, numbers, logic, procedures and words. The content of each category is relatively broad, and there are also overlaps between different categories. Sometimes, the problems discussed in this category may be touched somewhere in the next category. For each problem, the author tries to start from an interesting story and start around the story, so that readers can solve the problem happily and stimulate their extraordinary thinking under the emotional coordination.

Each question in this book is accompanied by a brief sketch drawn by Canadian painter Mr. Jim Green, followed by a description. These explanations have deepened the problem step by step and brought us into the colorful and confusing kingdom of modern mathematics.

In the eyes of ordinary people, mathematics is often inscrutable and boring, but in Gardner's works, abstract mathematical problems become interesting. For example, if God is omnipotent, can he make a stone that he can't move? Because God is omnipotent, he can make any kind of stone, so God can make stones that he can't move, so God is not omnipotent-he can't even move his own stones. Whether and how God exists is originally a metaphysical question. So ask, inexplicably solved-really weird. This interesting question is just "Aha! It's just an example in the book A brainwave.

Advanced topics such as number theory, graph theory, probability theory, group theory, matrix, combinatorial analysis, affine geometry, projective geometry, differential science, algorithm theory, topology, etc. have always been regarded as "Chun Xue", and ordinary popular science writers always feel very headache and dare not touch it. Martin gardner, on the other hand, excavated a lot of treasures from it, which made him surpass his peers and be unique. In this respect, even Burleiman, a famous mathematical science writer in the Soviet Union, can't compare with him.

Surprisingly, martin gardner himself has never received a "formal higher mathematics education". He can become an expert because of his love for pure intellectual activities, which makes his articles full of magic.

Gardner's language is humorous, his writing is vivid and he understands the reader's psychology. His articles can meet the needs of all social strata. Aha! A brainwave is very interesting, elegant and popular, and you can "catch" it at a glance, and you don't need a lot of preparatory knowledge, so you can't help itching.

Ⅲ. Notes on Aha Brain Wave

Aha, a brainwave

This is an Olympic Mathematics book, which talks about many interesting but not difficult math topics with cartoons in the middle. It is humorous but not unreasonable. After reading it, I had an epiphany.

One day, Ms. Wei greeted a passing taxi in new york.

The lady talked endlessly on the way to her destination, which bored the driver. The driver said, "Excuse me, madam! I didn't hear a word you said. My ears are deaf, and my hearing aid has been useless all day. "

The lady stopped nagging after listening. When she got off the bus, she suddenly realized that the taxi driver had cheated him. How did she know? An alert lady

This story about a lady and a taxi is a representative example in daily life and science. A confusing situation, when you got on the bus, what was the first thing you said? Of course, this is your destination, but if the driver's cab is deaf, how does he know you want it?

Where are you going?

The real problem lies behind. A taxi driver picked up a passenger who was going to Kennedy Airport in front of waldorf in new york City. The traffic was very heavy along the way. The driver ran for 80 minutes at an average speed of 30 kilometers per hour, and the driver charged the fare accordingly. Upon arrival, the driver just picked up another passenger who was going to the Waldorf tube. The driver drove back to the hotel at the same speed and route, but this time it took 1 hour and 20 minutes. Why?

It may take some time for most people to realize that 80 minutes and 1 hour 20 minutes are equal. Try this interesting and confusing topic for your friends!

Here's another question involving taxi drivers:

You are a taxi driver. You have a yellow-black car that has been used for seven years. The wiper and carburetor on the windshield need to be adjusted. The water tank can hold 20 gallons of water, but it is only full at present. Ask you: How old is the driver?

Although this question is logically perfect and consistent, it is more deceptive than the last one. Because I told you from the beginning that you are a driver, your age is the driver's age.

This is the secret of this book and the reason why I like it. What do you think of this book after reading the introduction of this number?

Ⅳ Aha, 400 words after reading a brainwave.

Everyone will grow up, from ignorance to knowledge, from short to high. In the process of growing up, I think everyone must have a lot of troubles! When I was in the first grade, there was a very annoying thing. What is that? Let me tell you about this trouble. That year, it happened to be the summer vacation, and my parents took me to Australia to play. To go to Australia, you have to fly and sleep on the plane. I can't sleep well because it's noisy and bright. What can I do? At this time, my mother told me that there was an eye patch to wear on the plane, and I just didn't want to be distracted. Although I did as my mother said, the seats were small and crowded, and now there is another worry. What happened? I had a brainwave and a method flashed before my eyes. I am the closest, and this is the best way. You see, I put my hand down, fastened my seat belt, leaned back, put the quilt around my neck, put down my blindfold and slept quietly. The next day, I found that I really slept in my original seat and didn't stagger. I finally solved this trouble! In the second summer vacation, I reported "New Oriental", "Challenge 100" and swimming training. "New Oriental" and Swimming No.5 have time overlap. I kept muttering to myself, "If I go to New Oriental, I can swim in 10 days. If I take swimming lessons, "New Oriental" may not have time to make up lessons. I am on the horns of a dilemma. Finally, I think: swimming on 10 is more important, and it doesn't matter when making up lessons. I should take a swimming class! I hurried to ask my mother for advice, and my mother said the same thing. I'm so happy, which shows that my decision is reasonable! On your way to growth, you will certainly encounter many troubles! When I was growing up, I encountered many troubles, but I solved them all. During my growing up, my troubles became less and less. I learned to stand on my own feet and how to overcome difficulties. I believe I will become more and more mature and self-reliant. In the end, it will grow into a full-fledged eagle and fly freely and happily in the blue sky.

Ⅳ "Aha! What is the content of this book?

Martin? Gardner is very knowledgeable, "aha! The book "A brainwave" is rich in content, from the simplest arithmetic and algebra to unfathomable topology and super-difference, covering a wide range and attracting attention with many "hot spots". Every reader can "get what he needs" and find interesting chapters suitable for his education level. The contents of this book can be divided into six categories: combination, geometry, numbers, logic, procedures and words. The content of each category is relatively broad, and there are also overlaps between different categories. Sometimes, the problems discussed in this category may be touched somewhere in the next category. For each problem, the author tries to start from an interesting story and start around the story, so that readers can solve the problem happily and stimulate their extraordinary thinking under the emotional coordination.

Every question in this book is accompanied by the Canadian painter Jim? Mr. Green's brief sketch is explained after the question. These explanations have deepened the problem step by step and brought us into the colorful and confusing kingdom of modern mathematics.

In the eyes of ordinary people, mathematics is often inscrutable and boring, but in Gardner's works, abstract mathematical problems become interesting. For example, if God is omnipotent, can he make a stone that he can't move? Because God is omnipotent, he can make any kind of stone, so God can make stones that he can't move, so God is not omnipotent-he can't even move his own stones. Whether and how God exists is originally a metaphysical question. So ask, inexplicably solved-really weird. This interesting question is just "Aha! It's just an example in the book A brainwave.

ⅵ Aha, 400 words after reading a brainwave. . .

Aha, after watching a brainwave.

This is an Olympic Mathematics book, which talks about many interesting but not difficult math topics with cartoons in the middle. It is humorous but not unreasonable. After reading it, I had an epiphany.

One day, Ms. Wei greeted a passing taxi in new york.

The lady talked endlessly on the way to her destination, which bored the driver. The driver said, "Excuse me, madam! I didn't hear a word you said. My ears are deaf, and my hearing aid has been useless all day. "

The lady stopped nagging after listening. When she got off the bus, she suddenly realized that the taxi driver had cheated him. How did she know? The Alert Lady tells the story of a lady and a taxi, which is a representative example in daily life and science. What was the first thing you said when you got on the bus? Of course, this is your destination, but if the driver's cab is deaf, how does he know you want it?

Where are you going?

The real problem lies behind. A taxi driver picked up a passenger who was going to Kennedy Airport in front of waldorf in new york City. The traffic was very heavy along the way. The driver ran for 80 minutes at an average speed of 30 kilometers per hour, and the driver charged the fare accordingly. reach

After that, the driver just received another passenger who was going to Waldorf Astoria to take care of it. The driver drove back to the hotel according to the speed and route just now, but this time it took 1 hour for 20 minutes. Why?

It may take some time for most people to realize that 80 minutes and 1 hour 20 minutes are equal. Try this interesting and confusing topic for your friends!

Here's another question involving taxi drivers:

You are a taxi driver. You have a yellow-black car that has been used for seven years. The wiper and carburetor on the windshield need to be adjusted. The water tank can hold 20 gallons of water, but it is only full at present. Ask you: How old is the driver?

Although this question is logically perfect and consistent, it is more deceptive than the last one. Because I told you from the beginning that you are a driver, your age is the driver's age.

This is the mystery of this book and the reason why I like it. What do you think of this book after reading the introduction of this number?