1 thought on “What is the Euler question?”

  1. Big mathematician Euler also attaches great importance to the education of mathematics. He often goes to middle school to teach mathematical knowledge and write mathematical textbooks for students. In particular, in 1770, the elderly Euler's eyes were blind, and he still missed the "Comprehensive Guide to Booking Mathematics" to students. After the publication was published, it was quickly translated into several foreign characters. Until the 20th century, some schools still used it as basic textbooks.

    In order to do a good job of the education of mathematics, Euler devoted himself to many primary mathematical issues, and also compiled many interesting mathematics questions. Perhaps because Euler is one of the greatest mathematicians in history, these topics are particularly widely circulated. For example, in mathematical extracurricular books in various countries, the following mathematical problems called "Euler" can be seen below.

    "The two farmers brought 100 eggs to the market for sale. The number of eggs between the two was different, but they made the same money. The first farmers said to the second farmer: 'If I have so many eggs, I can earn 15 copper coins.' The second farmer replied: 'If I have so many eggs, I can only earn 623 copper coins. How many eggs are brought? "

    In history, it is not uncommon to give an equivalent relationship from the form of dialogue. For example, in the 3rd century BC, the ancient Greek mathematician Ou Guli had edited a question of dialogue between donkeys and mules:

    The cargo is too heavy and can't stand it. The mule said to it: 'What are you grieving it! I am heavier than you. If the goods you carry give me 1 pocket, the goods I put on the goods will be 1 heavier than you are 1 heavier than you. Be more; and if I give you a pocket, we are just as many as much. 'Ask the donkeys and the mules to put a few pockets each? "

    12 century, Indian mathematician Po Shiro also edited A similar exercise:

    "Someone said to a friend: 'If you give me 100 copper coins, I will be twice more richer than you. Copper coins, I am 6 times richer than you. 'Ask how many copper coins they have each? "

    , but the" Euler question "has made new ideas, because the two" if "out of the two" if "came out of the" if "the" if "came out" The answer to the number of answers can be at all to say that the equivalent relationship contained in the question is difficult to find, and the problem of solving the problem is different from the above two questions.

    It is a solution provided by Euler.

    I assume that the number of eggs of the second peasant woman is M times of the first peasant woman. Because the last two made a lot of money. Therefore, the price of the first farmers selling eggs must be M times of the second peasant woman.

    . If the two farmers have swapped the eggs they brought before they are sold, then the number of eggs with the first peasant woman and the price of the sale of eggs will be M times. In other words, the number of money she earns will be M2 times that of the second peasant woman.

    then M2 = 15: 623.

    This After the negative value is left, M = 3/2, that is, the ratio of the number of eggs brought by the two people is 3: 2. In this way, the total number of eggs is 100, and it is not difficult to calculate the answer to the question.

    This is not easy to come up with this clever solution. The consistently cautious Euler couldn't help but praise his solution as "the most clever solution."

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