"Where there is mathematics, there is beauty!" -Plocque Ras, an ancient Greek mathematician. Speaking of beauty, people can't help but think of the beauty of music that "goes around the beam for three days"; Or think of the artistic beauty of "wonderful workmanship" or the natural beauty of "beautiful scenery" ... But now most students will not associate high school mathematics with beauty, which also explains the lack of aesthetic education in mathematics to some extent. According to the investigation and analysis, students' interest in mathematics is now based on their excellent grades in junior high school mathematics. After entering high school, the difficulty of mathematics suddenly increased, which led to a sharp decline in the mathematics scores of most students, thus suddenly losing their love for mathematics. The sudden change from love to hate is due to their "fake" interest in mathematics. Infiltrating aesthetic education into mathematics education can stimulate students' interest in mathematical truth, which is the best teacher for students. People's love of beauty is particularly prominent in adolescence. Mathematics teachers should seize this best opportunity to reveal the beauty of mathematics to students, so as to delight students' mood, stimulate students' interest, cultivate students' temperament, mold students' souls, and then let students understand, appreciate and create the beauty of mathematics. Klein, a great mathematician, said, "Music can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can touch people's hearts, philosophy can make people gain wisdom, science can improve material life, but mathematics can give them all." What is the beauty of mathematics? Russell said: "Mathematics has not only truth, but also the highest beauty. The true beauty of sculpture is a kind of cold and serious beauty! " The beauty of mathematics is different from artistic beauty such as painting and music, and also from natural beauty such as flowers and rainbows. It is the perceptual and rational expression of scientific strength, the expression of human essential strength through mathematical thinking structure, a true beauty, and a scientific beauty that reflects and can transform the objective world. Mathematical beauty is not only harmonious in form, but also rigorous in content. Not only the beauty of concrete formulas and theorems, but also the beauty of structure and integrity; There are both the beauty of conciseness and exquisiteness of language and the beauty of strange unity of method and thought; There are beauty of logic and abstraction, beauty of creation and beauty of application. As a new generation of teachers, we should constantly explore the beauty of mathematics, constantly teach the beauty of mathematics, let students feel the beauty of mathematics, and thus stimulate students' interest in learning mathematics. Under the background of new curriculum standards, teachers are required to carry out aesthetic education in the process of mathematics education to cultivate students' aesthetic ability, thus forming a beautiful mind. How to carry out aesthetic education in mathematics teaching, the author has a lot of feelings in the teaching process in recent years. One: Simple Mathematical Beauty Einstein said, "Beauty is simple in essence." And the beauty of simplicity in mathematics is almost everywhere. Euler's formula-"V+F-E = 2" is a model of simplicity and beauty. There are endless convex polyhedrons in the world, but their number of faces, vertices and edges all conform to this simple formula. In addition, the well-known Pythagorean theorem uses a simple quadratic formula to describe the relationship between the right side and the hypotenuse of all right triangles. The basic theorem of calculus describes the relationship between definite integral and original function with concise formula. Throughout the history of mathematics, great mathematicians have been pursuing simpler and more universal theorems all their lives. Some of them, such as Goldbach conjecture with concise beauty, are being broken by countless math lovers. Chen Shengshen, a famous mathematician in China, said: "Simplicity and elegance are overwhelming in mathematics." As a new generation of educators, we should be good at excavating the beauty of simplicity in teaching materials, summarizing the simplicity and generality of mathematical formulas in time, so that they can feel the beauty of simplicity in mathematics and grasp their hearts. 2. Unified mathematical beauty is a vast universe, including everything. There are endless celestial bodies in the universe, and exploring the mysteries of the universe has always been the pursuit of human dreams. In the face of countless celestial movements, people have calculated their trajectories, which are either ellipses, hyperbolas or parabolas, and can be unified mathematically in just one sentence: "The ratio of the distance from a fixed point to a fixed straight line is the trajectory of a constant e ... The trajectory at that time was elliptical; The trajectory at that time was a parabola; The trajectory at that time was a hyperbola. " The beauty of unity in mathematics can be seen. In addition, in solid geometry, the surface area and volume formulas of the platform harmoniously unify the surface area and volume formulas of the vertebral body and the cylinder. In trigonometric function, the universal formula uses tangent to represent sine, cosine and tangent uniformly. How unified and beautiful! The beauty of unity in teaching is particularly important. Teachers should not only be good at discovering and summarizing the beauty of unity, but also teach students in time. It is in the process of introducing and learning all kinds of unified beauty that students can analyze and compare, thus breaking through the difficulties and feeling the unified beauty of mathematics in essence. 3. Strange Mathematical Beauty Pythagoras said, "Everything has a number." He harmoniously unified nature and numbers. Once, his friend asked him, "Is it related to numbers that I make friends with you?" He replied, "A friend is a beautiful image of your soul. Be close to 220 and 284. " Looking at the puzzled people, Pythagoras explained that all true factors of 220 1, 2, 4, 5, 10,1,20, 22, 44, 55,1/kloc. And the sum of all the true factors of 284, 1, 2, 4, 7 1, 142 is exactly 220. This is the intimacy number. True friends are just like them. The strange beauty of mathematics touched all the audience, and many scholars have been talking about affinity numbers so far. In addition, he described a happy marriage with a perfect number-the sum of all true factors is equal to itself. In high school mathematics, when the value of eccentricity e is 0.9999, the trajectory is still ellipse; But when it becomes 1, the trajectory is parabolic; When it becomes 1.005438+0 again, the trajectory becomes a hyperbola. It is strange that a little change leads to a completely different image. There is indeed a lot of strange beauty in mathematics, and students will feel the magic of mathematics through our careful excavation. Fourth, the new curriculum standard of natural mathematics beauty puts forward: "Mathematics comes from life and is applied to life." Mathematics in life can be seen everywhere, for example, the golden section number is 0.6 18, which is the most harmonious proportional relationship and has high aesthetic value. The ratio of navel height to total human height is close to or equal to 0.618; When the host hosts the program, he stands in the prime location of the stage, which is not boring and has the best sound communication effect; In architectural modeling, the waistline or decorations arranged at the golden section can make the whole building look magnificent and elegant. The honeycomb is hexagonal, and the angle is also very accurate, obtuse 109 32'. This kind of nest not only saves materials, but also is strong and firm, which amazes engineers! More surprisingly, bees also know the shortest distance between two points. After randomly collecting nectar from flowers, bees know to take the most direct route back to the hive. Being good at using mathematical examples in nature and life to show the perfect combination of mathematical beauty and natural life can often make students feel the practicality of mathematics and make them really interested in mathematics. Some people say that if mathematics is read as a collection of poems, then any mathematics course in front of us will suddenly change from a pile of dead formulas to a collection of poems full of harmony, exquisiteness and symmetry. As long as the beauty of mathematics is integrated into the teaching of mathematics, not only will our teaching become relaxed and natural, but students will also be relieved, constantly improve their interest in mathematics, and make teaching and learning harmonious, perfect and unified. It is true that the beauty contained in mathematics is profound, and the beauty of mathematics is not only the above points, but also runs through almost all aspects of mathematics. In addition, the symmetry, similarity, harmony and transitivity of mathematical theorems and formulas are all manifestations of beauty; Sometimes even mathematical problems show beauty, and the disintegration method also exudes beauty. Of course, mathematics is not like a good piece of music or an outstanding work of art, and its beauty can be tasted at a glance. Especially for students with heavy schoolwork, due to the limitation of experience level, basic knowledge and mathematical training, it is difficult to taste all kinds of mathematical beauty. This requires teachers to study hard, constantly discover beauty from relatively boring textbooks, and seize the opportunity to guide and cultivate them. Looking forward to the future educational trend, the combination of aesthetic education teaching and mathematics teaching is necessary and inevitable, which can not only awaken students' declining interest in mathematics, but also improve their aesthetic ability, thus cultivating the next generation's ability to create beauty.