Math Paper Today, in our math club, the teacher studied an interesting topic for us. In fact, it is a somewhat complicated topic of finding laws. The title is like this: "There is a column number: 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 4, 3. What is the sum of the top 240 numbers in this column? " As soon as I got the topic, I thought, this topic must be done according to law. At first, I tried to sum in groups of three, 6,5,10,9, 12, 15, 14. In this way, these figures have their own characteristics, and the key is that they can't find a suitable law. So, I found a group of four to sum, 8, 10, 12,16,20. After a careful look, it seems that there is no rule, so I have to try to find a group of five to sum, 9, 14, 19, 24 ..., so obviously they are equal series, I am very happy, and then 240÷5=48 (group), a group of five, (6544. (4, 5, 6, 5, 4) ... Then we can find the sum of the last term, 9+47×5=244, and divide the sum of the first term and the last term by 2, (9+244)×48÷2=6072. That's it! Then, I found that the first number at the beginning of each group is exactly 1, 2,3,4 ... 48, so I came up with another method, (1+48) × 48× 2+(2+49 )× 48× 2+. It is reasonable to think so, and it is also a clear and practical method! Later, it was found that when there were n groups, his sum was also (1+2+3+4+ and ... +n) × 5+4n = the number of n groups you needed, for example, (1+2+3+4+...+48 )× 5. Although this rule is somewhat abstract, it is simpler than the other two methods if you understand it yourself. All I did was three of them. In fact, there are many other ways, but as long as you find the law and solve the mystery yourself, you will find it very interesting. Mathematics in life "Anything can become mathematics for me." 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 300 yuan coupons to buy a navy Li Ning cotton-padded jacket of 298 yuan, 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! The golden section is no stranger to the golden section! Since the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, modern mathematicians have come to the conclusion that Pythagoras school had touched and even mastered the golden section at that time. In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion. When Euclid wrote The Elements of Geometry around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section. After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred. It was not until the19th century that the name golden section gradually became popular. The golden section number has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s. Perhaps, we have learned a lot about the performance of 0.6 18 in science and art, but have you ever heard that 0.6 18 has an indissoluble bond with the fierce and cruel battlefield of gunfire and bloodshed, and also shows its great and mysterious power in the military? Napoleon the Great, a lean man, never thought that his fate would be closely linked with 0. 18. June, 18 12, is the coolest and pleasant summer in Moscow. After the battle of Borokino, which failed to destroy the Russian army, Napoleon led the army into Moscow at this time. At this time, he is full of ambition and arrogance. He didn't realize that genius and luck were disappearing from him at this time, and the peak and turning point of his career came at the same time. Later, the French army withdrew from Moscow in frustration in the heavy snow and howling cold wind. Three months of triumph, two months of climax and decline, from the time axis, when the French emperor overlooked Moscow through the flame, his foot just stepped on the golden section. The Parthenon in ancient Greece is a world-famous perfect building with an aspect ratio of 0.6 18. Architects found that the palace designed according to this ratio is more magnificent and beautiful; To design a villa will be more comfortable and beautiful. Even if a door and window is designed as a golden rectangle, it will be more harmonious and pleasing to the eye. Interestingly, this kind of figure can be seen everywhere in nature and people's lives: the navel is the golden section of the whole human body, and the knee is the golden section from the navel to the heel. The aspect ratio of most doors and windows is also 0.618. On some plants, the included angle between two adjacent petioles is 137 degrees 28', which is exactly the included angle between two radii that divide the circumference into 1: 0.6 18. According to research, this angle has the best effect on ventilation and lighting of the factory building. The golden section is closely related to people. The latitude range of the earth's surface is 0-90 degrees. If divided into the golden section, 34.38-55.62 is the golden zone of the earth. No matter from the aspects of average temperature, annual sunshine hours, annual precipitation and relative humidity, it is the most suitable area for human life. Coincidentally, this region covers almost all the developed countries in the world. Observe life more, and you will find the wonderful mathematics in life!