One. The beauty of simplicity in mathematics.
The beauty of simplicity in mathematics is expressed in form, that is, the external expression of mathematical beauty, which is the beauty presented in the external structure of mathematical theorems and mathematical formulas (or expressions). The main feature of formal beauty is simplicity. For example, the formula given by Euler: V-E+F = 2 is a model of "simple beauty". No one can tell how many polyhedrons there are in the world. But their vertex number v, edge number e and surface number f must obey the formula given by Euler. Such a simple formula sums up the identity characteristics of countless polyhedrons, which is amazing. In mathematics, there are many theorems with simple form, profound content and great effect, such as Euler formula.
For example, the circumference formula of a circle: C=2πR The circumference of any circle satisfies this formula. Newton, a British scientist, summed up the quantitative relationship among force, mass and acceleration with F=ma. For another example, the German scientist Einstein revealed the transformation relationship between mass and energy in nature with E = MC 2; Here F=ma and E = MC 2 are very concise in external form.
Second, the beauty of symmetry.
Most beautiful curves are the combination of mathematical beauty and harmony. Such as the four-leaf rose line, logarithmic spiral and the prestigious Mobius curve obtained from nature. The harmonious beauty of Mobius curve is not only limited to its appearance, but also reflected in the highly restrained harmonious beauty of "constructing one-dimensional space in two-dimensional space" Twist one end of a long piece of paper and stick it with the other end, so that when an ant starts from any point along one side of the paper, it can go through all the routes on both sides of the paper and return to the origin. This magical "two-in-one" structure embodies a great philosophy of combining mathematics with communication-turning enemies into friends, and friends and relatives are true.
Third, unified beauty.
The beauty of unity reflects some similarity, relevance or consistency of aesthetic objects in form or content, which can give people a harmonious aesthetic feeling as a whole. The unity of mathematical objects is usually manifested in the unity of mathematical concepts, laws and methods, the unity of mathematical theories and the unity of mathematics and other sciences. Unity of mathematical theory. In the historical process of mathematical discovery, there are two trends: differentiation and integration. The unity of mathematical theory is mainly manifested in its holistic trend. Euclid's Elements of Geometry simplifies some spatial properties into several abstract concepts, five postulates and five axioms, thus producing an elegant deductive theoretical system and showing a high degree of unity. Bhurki School's Principles of Mathematics reorganized all branches of mathematics with structural thoughts and languages, revealed the internal relations of mathematics in essence, made it an organic whole, and gave people beautiful enlightenment in the high unity of mathematics.
Fourth, Chi Mei
/kloc-Euler, the greatest mathematician in the 8th century, proved that Fermat's theorem holds when n = 3,4. It turned out that when n