"For me, anything can become math." The mathematician Descartes once said this. "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the complexity of daily use, and mathematics is everywhere." Hua, a famous mathematician in China, once reached such a conclusion. Indeed, as the two predecessors said, mathematics is closely related to our lives, and the footsteps of mathematics are everywhere.
2006 is coming to an end, and a new year -2007 is coming. Walking on the busy street, promotional signs of "400 for over 400" and "300 for over 300" can be seen everywhere. "This is really affordable!" Consumers flock to shopping malls, which are crowded with people, and snapping up is a common occurrence. This situation really makes people feel that they have returned to the era of material scarcity. In fact, the merchants have already laid their wishful thinking in their hearts. As the saying goes, only buy at a loss, don't sell at a loss, and the "400 yuan coupon for over 400 yuan" is just a sales promotion method for merchants, which hides mathematical problems, trade secrets and many mysteries.
Last year, our family of three also "shopped" in the shopping mall on the occasion of the Chinese New Year. At that time, more than 400 coupons were sent to 400 yuan. First, I bought my father an apple leather jacket with 980 yuan and sent a shopping voucher to 800 yuan. We didn't waste too much. We spent 298 yuan to buy a navy Li Ning cotton-padded jacket, and used 488 of the remaining 500 yuan coupons to buy a Taizilong men's suit (as it is a shopping voucher, no change). How much cheaper? 298+488+980= 1766 (yuan)-this is the money that needs to be spent when there is no discount. 980/ 1776, the discount is about 55%.
My aunt and uncle used to be in the clothing business, and I know something about the relationship between the purchase cost and the sales price of clothing. The purchase price of clothing generally only accounts for 20%~30% of the suggested retail price. With the intensification of competition and the promotion of shopping malls, in order to maintain profits, merchants or manufacturers continue to raise the suggested retail price of clothes. As a consumer who saw on TV a few days ago said, the suggested retail price of a pair of nylon trousers of the same style of a certain brand was only 299 yuan three years ago, and this year's price tag has become 999 yuan. Based on this calculation, the purchase price is only about 10%~20% of the market price. Even with a 55% discount, businesses can still earn 30% to 50% gross profit.
Advertising, advertising, advertising. Many people rush to buy and shop, and the flow of people in shopping malls increases, and the sales of goods also increase rapidly. Just when the flow of people is three times as usual, another math problem comes. Suppose a commodity is sold at a 20% discount when there is little traffic. 20% off the purchase price, 20% off the purchase price, and 6% of the marked price becomes gross profit. Although you may only earn 30% to 50% with 400 yuan coupons for the same product over 400, the sales volume is at least three times that of usual. Calculated by 30% gross profit and triple sales, 3×3=9, compared with the usual 60% gross profit, you can earn 50% more in one day. Although the gross profit margin of each product sold in this way has decreased, the gross profit has increased due to the increase of sales volume, and because of the large sales volume, the capital turnover has been accelerated and additional income has been brought.
There are mathematics in commodity pricing and promotion, mathematics in shopping consumption, mathematics in house decoration, mathematics in sweater weaving ... In short, mathematics is everywhere in real life!
Win a coin skillfully
I remember one day in the summer vacation, we went to my uncle's house and had a good time. My uncle came up with 10 coins and said, "Do you want these coins?" "Of course I want to!" Everyone answered with one voice. I looked at my uncle, a bit like a monk-scratching his head. I'm curious about what medicine my uncle is selling in the gourd. "If you want these coins, you must answer my question. Whoever answers correctly will get the coin. " Then my uncle asked a question: "How to put 10 coins into three cups, so that the number of coins in each cup is odd, and who can find the most way?"
After listening to my uncle's topic, everyone thought hard. I saw my cousin walking around in the living room, sitting in a chair and thinking calmly. Soon, I saw my sister find the material and try to do it. However, after doing it for a long time, my sister still didn't find a specific solution to the problem. In order not to be surpassed, I think with my head. Oh, if only I could get this coin!
After more than ten minutes, no one thought of what to do. My uncle saw this scene and said to us, "I'll give you a hint!" Learn to turn around a few times to solve this problem, don't ... ""Wait! " Words haven't finished, my cousin seems to think of something. I saw him pick up the coin of 10, first put the coin of 1 in the cup of 1, and then put three coins in the second cup. Seeing this, I can't help thinking: this method, which I have been thinking for a long time, simply won't work. There are six coins left, and six is an even number. I can definitely say, "This method. When my cousin put the remaining six coins in the third cup, I interjected, "This method is simply …" Before I finished, my cousin interrupted me. Cousin, you'd better watch me perform! " Cousin said proudly. I saw him pick up the cup of 1 and put the coin in the third cup. "This is the first method. "My cousin made a proud face." Oh! How stupid am I to give up at the thought of the third step? Really not worth it! "Then, my cousin did what he did for the first time, first put three coins in the cup of 1, then put five coins in the second cup, then put the remaining coins in the third cup, and finally put the coins in the first cup in the third cup. This completes the second method. According to this method, my cousin made 13 times in a row.
Seeing this, the uncle standing by clapped his hands and nodded, "I never thought that you, a kid, still had time to think." You won this time, and all the 10 gold coins are yours. " Uncle praised his cousin and touched his little head. "However, light rain, you must work harder. This time, even my cousin beat you. Remember, think more about everything and don't give up easily. "
Yes, uncle is right. Think more about everything and don't give up easily. If I hadn't given up the third step just now, I would have used my brain to solve the problem again. I really want to work harder in the future, learn math well, master math well, and learn to use math flexibly in my life.
The Origin and Development of Numbers
Humans are the product of animal evolution, and there was no concept of quantity at first. However, the developed brain's understanding of the objective world has reached a more rational and abstract level. In this way, in the long life practice, out of the need to record and distribute daily necessities, the concept of number has gradually emerged. For example, a wild animal is captured, which is represented by 1 stone. If you catch three heads, put three stones. "Knotting knots" is also something that many close ancient humans have done. There is a record of "tying the knot to govern the country" in the book of changes. Legend has it that the ancient Persian kings tied knots with ropes to count the days of war. It is also a common method used by the ancients to carve or hide the bark with sharp tools or count it on the ground with small sticks. When these methods are used much more, the concept of number and the symbol of counting are gradually formed.
The figures in ancient Rome were quite advanced, and now many old wall clocks are often used. In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for/kloc-). They can be combined to represent any number according to the following laws:
1. Repetition: How many times a Roman numeral symbol is repeated means several times this number. For example, "three" means "3"; "XXX" means "30"
2. Add right and subtract left: add a symbol representing big numbers to the right of the symbol representing small numbers, indicating that big numbers are added with small numbers, such as "VI" for "6" and "DC" for "600". A symbol representing a small number is attached to the left of the symbol representing a large number, indicating a number in which a large number is subtracted from a small number, such as "IV" for "4", "XL" for "40" and "VD" for "495".
3. Add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number. For example, "XV" means "15000" and "CLXV" means "165000".
At present, the internationally used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over Europe, gradually evolving into today's Arabic numerals.
With the needs of production and life, people find that it is not enough to express it only by natural numbers. If five people share four things when distributing prey, how much should each person get? So the score is generated. China's academic score is earlier than that of Europe 1400 years! Natural numbers, fractions and zeros are usually called arithmetic numbers. Natural numbers are also called positive integers.
With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, advance and retreat, rise and fall, east and west. To represent such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers. If you add a positive score and a negative score, they are collectively called rational numbers. With these digital representations, people find it much more convenient to calculate.