The beauty of mathematics can be summarized as: simplicity, harmony and strangeness.
First, concise beauty? Chen Shengshen, a famous mathematician, said: "For mathematical experts, beauty and harmony are really equally respected. In the abstract mathematical world, the requirements of simplicity and elegance are almost overwhelming. " The beauty of simplicity in mathematics can be said to be everywhere. For example, many definitions in mathematics, such as formulas, all embody simple characteristics. For example, when teaching the definition of parallelogram, students are allowed to define it freely after full observation, and then through comparison, it is revealed that the definition of "equilateral quadrilateral is called parallelogram" is impeccably simple. The concise beauty of this mathematical language gives people a bright and concise aesthetic feeling. ?
The beauty of simplicity in mathematics is not only reflected in calculation and proof, but also widely used in real life. For example, people use bank cards instead of large amounts of cash. In a word, mathematics can abstract the laws and rules of nature and then turn them into corresponding axioms, laws or concepts. It shows the ideal space corresponding to the real world, but higher and better than the real world, shows the concise beauty of mathematics, and gives people a strong experience and feeling of beauty.
? Second, harmonious beauty? The harmonious beauty of mathematics is a unified, orderly and non-contradictory symmetrical beauty, which is not only reflected in the symmetry of formulas and figures, but also has its unique charm in many problems. Beautiful melody is inextricably linked with numbers; All spatial figures can be simplified and abstracted into points, lines, surfaces and bodies, which fully embodies the beauty of unity and harmony in mathematics. The golden section in geometry has become a symbol of all good things in people's hearts with its harmonious proportion; As outstanding representatives of symmetrical beauty in geometric figures, circles and balls bring people colorful natural beauty; The proof of butterfly theorem enriches the connotation of beauty in mathematics from another angle, which is the geometry of beauty. The harmonious beauty of algebra is no less than that of geometry. Can you say that multiplication formula, binomial theorem, linear equation, neutral angle formula of trigonometric function, difference angle formula and Yang Hui triangle are not beautiful? The image of geometric beauty and the charm of algebraic beauty complement each other and together constitute the harmonious beauty of mathematics. ?
The harmony of mathematics also shows that it can find the best argument for the harmony of nature, the harmony of life phenomena and the harmony of human beings. Taking the blood circulation of animals as an example, the process of blood transportation to the whole body well embodies the harmonious beauty of mathematics.
? Third, Chi Mei? Many discoveries in mathematics are amazing. Singular beauty is another embodiment of mathematical beauty, which fully demonstrates the originality and novelty of mathematical thinking methods. Geometry and algebra used to be considered as two different branches, moving in two parallel tracks and never intersecting. Finally, one day, people suddenly discovered that a simple quadratic equation actually contains a beautiful conic curve. Algebra and geometry were originally a family. This amazing discovery gives people a feeling of being suddenly enlightened. Isn't this the charm of mathematics? ?
Mathematics gives people a novel aesthetic feeling with its unique form. Influenced by objective conditions, nobody thought about the bisector of an angle until the middle of19th century, which made Morley's theorem one of the most surprising theorems in elementary geometry. Many interesting properties can be found in some very common numbers, such as: 3× 4 =1233× 34 =122333× 334 =11223333× 334 = 65434.