academician zhou xiangyu performed "poker magic" to help primary school students appreciate the beauty of ancient mathematics
2024-09-03
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"it's so hard for me to do math problems every day. do academicians do math problems like us every day?" "why did the ancients study mathematics that seemed useless at the time?" "mathematics is so difficult, what makes him continue to study it?"... upon learning that zhou xiangyu, an academician and mathematician of the chinese academy of sciences, is about to come to school, students of banchang primary school in dongcheng district, beijing, have raised questions one after another. on the afternoon of september 2, zhou xiangyu walked into the senior grade department of banchang primary school in anticipation of the students, shared ancient mathematical ideas with the students, and led the students to appreciate the beauty of mathematics.
this is one of the series of activities of "2024 scientist spirit leading the first lesson of the new school year". in the new autumn semester of 2024, the beijing association for science and technology and the beijing news invited the "beijing propaganda team of scientist spirit" composed of academicians, veteran scientists, and young scientific and technological workers to visit more than 10 primary and secondary schools in beijing from september 1 to 2 to communicate with students face to face, convey the scientist spirit to children, and stimulate their curiosity to explore the mysteries of science.
zhou xiangyu visited banchang primary school in dongcheng district, beijing to share ancient chinese mathematical ideas. photo by beijing news reporter li muyi
perform magic tricks and discover the mathematical rules behind them
"witness the moment of miracle... throw away the worries and keep the good luck... magically, the hidden card and the last card left become the same card!" at the lecture, zhou xiangyu brought an enlarged version of "playing cards" that he had printed, and led the students on the podium to relive the poker magic on the 2024 spring festival gala.
"how do you put a playing card that's been torn in two together?" he explained the method as he did it: fold any 4 stacked cards in half and tear them apart, then stack the two stacks together with their backs facing you, and then randomly pick up a few cards from the top and place them underneath.
after several rounds of operation, zhou xiangyu guided the students to reveal the rules behind the magic step by step. "it seems that the cards are messy, but no matter when and whose cards they are, the first card and the fifth card can actually form the same card. similarly, the second card and the sixth card, the third card and the seventh card, and the fourth card and the eighth card can also form the same card."
"magic is amazing, but behind it is the ancient chinese mathematical idea about congruence." zhou xiangyu told the students that this periodic pattern means that the two numbers corresponding to the four pairs of cards have the same remainder when divided by 4, which is called (modulo 4) congruence in mathematics.
in order to help students understand the same principle, zhou xiangyu also told the story of "han xin counting soldiers". han xin had a special way to count the number of soldiers, which was to have the soldiers line up in three columns, then in five columns, and finally in seven columns. "as long as he knew the number of soldiers in the last row of the three columns, he could calculate the exact number of soldiers in the team. in fact, he also applied the same mathematical law."
zhou xiangyu performed magic at the lecture and revealed the mathematical rules behind it. photo by beijing news reporter li muyi
citing classics to explain the contribution of ancient chinese mathematics
"mathematics is a subject that our people are good at. mathematics should be comprehensive." zhou xiangyu believes that ancient chinese mathematics is a fusion of the abstract and the concrete. at the lecture, zhou xiangyu started with interesting mathematical stories and led the students step by step into the door of ancient chinese mathematics.
the "pythagorean theorem" is a well-known mathematical principle among students. however, what most people don't know is that the pythagorean theorem and its proof have actually been systematically and comprehensively explained in the ancient chinese book "zhou bi suanjing".
"so fold the square to make the hypotenuse 3, the leg 4, and the diameter 5." zhou xiangyu showed the original text in zhoubi suanjing about shang gao's idea of folding the square, as well as shang gao's proof of the pythagorean theorem: "after square it, take half of the square outside, circle it and make it three, four, and five." he also explained it to the students word by word, and pointed out the significance of shang gao's proof of the pythagorean theorem - "this opened the precedent for proposition proof."
"cutting and patching", "ringing and sharing the same plate", "side key"... in many cases, zhou xiangyu used pictures and graphs to explain to students, explaining the profound connotations of ancient chinese mathematical thought. the reporter noticed that many of these pictures were hand-drawn by zhou xiangyu himself, and the text deductions next to the pictures were also clearly handwritten.
in addition to the zhoubi suanjing, zhou xiangyu also quoted classics to show everyone the concepts, methods and contributions of ancient chinese classic mathematical works such as the xugu zhaiqi suanfa, the jiuzhang suanshu and the mozi jingxia 41, including the history of china's creation of the decimal system, the use of mathematical tools such as rules, standards and counting rods in ancient my country, as well as the calculation steps and rules of multiplication, division, square root and fractions, etc.
zhou xiangyu takes students to appreciate the beauty of mathematics. photo by beijing news reporter li muyi
inspire the spirit of exploration and share the integration of humanistic philosophy and ancient mathematics
while introducing the classical mathematical ideas of ancient china, zhou xiangyu also inspired students to skillfully apply these methods to conveniently solve mathematical problems in their current mathematics learning.
in addition to imparting "hard-core" mathematical knowledge, zhou xiangyu also focused on the relationship between ancient chinese mathematical thought and humanistic thought. he cited the example of wu jing of the tang dynasty, who wrote in "zhenguan zhengyao·fairness" that "law is the balance of the country and the standard of the times. the balance is used to determine the importance, and the standard is used to correct the crooked and the straight." this sentence emphasizes that national governance should be based on the law.
for example, in mencius, it is written: "the wisdom of li lou and the ingenuity of gongshu zi, without rules and regulations, cannot make the square or the circle; ... the way of yao and shun, without benevolent government, cannot bring peace to the world."
"without rules, there can be no order. this sentence has become a common motto. we should be a person and do things in an orderly manner." zhou xiangyu used simple language to convey to his classmates the principles of life and work contained in mathematical thinking.
zhou xiangyu told the beijing news that mathematics has played a very fundamental role in the process of human understanding of nature and the development of civilization, and it still does so today. "i hope that through dialogue with children, i can let them experience the fun and beauty of mathematics, and let them pay attention to mathematics, love mathematics, learn mathematics well, and use mathematics well in the future, which is very meaningful."
"our country's innovative development emphasizes two aspects: one is scientific and technological innovation, and the other is popularization of science. these are the two wings of innovative development. i think it is very meaningful to place popular science and scientific innovation on an equal footing. not only primary and secondary school students, but also many adults in society need to have some understanding of the development of science and technology, which requires a high level of popular science work. i hope that based on years of research experience, i can convey ancient china's mathematical ideas to more people more accurately." zhou xiangyu said.
beijing association for science and technology donated science and technology video products and books to banchang primary school. photo by beijing news reporter li muyi
after the lecture, the beijing association for science and technology presented the students with a series of products from the science and culture education program "big master" and science and technology books with rich content, aiming to broaden students' knowledge horizons and sow the seeds of science. it is reported that during the "2024 scientist spirit leading the first lesson of the school year", the organizer donated more than 1,000 popular science books to more than ten participating primary and secondary schools.
beijing news reporter feng qi
edited by wu hui, miao chenxia, proofread by jia ning
