1, golden ratio: φ is the golden ratio, which is defined as the ratio of the longer line segment to the original line segment, and is usually expressed as (1+√5)/2. The golden ratio is widely used in the fields of aesthetics, art and architecture, and is considered to be the perfect combination of proportion and symmetry.
2. Complex unit: on the complex plane, φ represents complex unit and satisfies φ 2 =- 1. This unit is usually used in quantum mechanics and complex analysis.
3. Angle: In geometry, φ represents an angle, usually a rotation angle or a polar angle. For example, in three-dimensional space, the angle of rotation around the Y axis is usually expressed by φ.
4. In circuit analysis and signal processing, φ represents phase angle; In number theory, φ stands for Euler function; In matrix theory, φ represents the eigenvalue of matrix, etc.
Mathematics can be divided into the following categories:
1, History of Mathematics: Studying the origin, development and influence of mathematics, as well as the evolution of various mathematical ideas, methods and schools.
2. Mathematical logic and mathematical foundation: the study of mathematical logic, mathematical foundation, mathematical philosophy and mathematical methodology involves basic concepts such as the essence, axioms, theorems and proofs of mathematics.
3. Number theory: study the nature, operation and structure of integers, as well as mathematical problems related to integers, such as prime numbers, divisors and fractions.
4. Algebra: Study the properties, structure, classification and relationships of algebraic systems, involving algebraic objects such as polynomials, matrices, vector spaces, groups and rings.
5. Geometry: study the shape, size, positional relationship and its properties of space, as well as mathematical problems related to geometry, such as Euclidean geometry and non-Euclidean geometry.
6. Topology: study topological space and its properties, involving topological properties such as spatial structure, connectivity and compactness.
7. Mathematical analysis: learn the basic concepts and properties of calculus such as limit, derivative and integral of functions, as well as the analysis of real numbers and complex numbers, function approximation and differential equations.
8. Probability theory and mathematical statistics: study the mathematical model and statistical methods of random phenomena, involving probability space, random variables, law of large numbers, central limit theorem, etc.
9. Applied Mathematics: Study the application of mathematics in various fields, such as physics, engineering, economy, biology, etc.