1. Two boys each ride a bicycle, starting from two places 20 miles apart (1 mile +0.6093 km) and riding in a straight line. At the moment they set off, a fly on the handlebar of one bicycle began to fly straight to another bicycle. As soon as it touched the handlebar of another bicycle, it immediately turned around and flew back. The fly flew back and forth, between the handlebars of two bicycles, until the two bicycles met. If every bicycle runs at a constant speed of 10 miles per hour and flies fly at a constant speed of 15 miles per hour, how many miles will flies fly?

answer

The speed of each bicycle is 10 miles per hour, and the two will meet at the midpoint of the distance of 2o miles after 1 hour. The speed of a fly is 15 miles per hour, so in 1 hour, it always flies 15 miles.

Many people try to solve this problem in a complicated way. They calculate the first distance between the handlebars of two bicycles, then return the distance, and so on, and calculate those shorter and shorter distances. But this will involve the so-called infinite series summation, which is very complicated advanced mathematics. It is said that at a cocktail party, someone told john von neumann (1903 ~ 1957, one of the greatest mathematicians in the 20th century). ) Put forward this question, he thought for a moment, and then gave the correct answer. The questioner seems a little depressed. He explained that most mathematicians always ignore the simple method to solve this problem and adopt the complex method of summation of infinite series.

Von Neumann had a surprised look on his face. "However, I use the method of summation of infinite series," he explained.

1, the correct view is that mathematics not only has truth, but also has extraordinary beauty-a beauty as cold and simple as sculpture, a beauty that does not need our weak nature to perceive, a beauty that is not as ornate as painting and music, and a strict perfection that only the greatest art can have.

-Russell (British philosopher, mathematical logician, the main founder of analysis, the advocate and organizer of the world peace movement. )

2. Being good at "retreating", retreating enough and retreating to the original place without losing its importance is a trick to learn mathematics well.

-Hua

3. Mathematics is a tool especially suitable for dealing with any abstract concept, and its power in this field is infinite. For this reason, a book about emerging physics, as long as it is not a pure experimental description, must be a math book in essence. -Dirac

Mathematics is the key to science and the beauty of the universe.

Kepler (German astronomer and optician)

5. Mathematics has two sides. On the one hand, it is a strict science of Euclid. From this perspective, mathematics is a systematic deductive science. On the other hand, mathematics in the process of creation looks like an experimental inductive science.

-Paulia (mathematician and math educator)

6. The same is true of "difficulty". Facing the cliffs, you can't see a crack in a hundred years, but you can cut it inch by inch and foot by foot with an axe. If you keep accumulating, a leap will come and a breakthrough will follow. -Hua (a world-famous mathematician, the founder and pioneer of China's research in analytic number theory, matrix geometry, canonical group and self-safety function theory. )

7. Think, keep thinking, wait for the dawn, and gradually see the light. If I have contributed to the world, it is not because of anything else, but because of my hard work and persistent thinking. -Newton (British mathematician, astronomer and physicist)