In two-dimensional space, if there are two points A(x 1, y 1) and B(x2, y2), the distance of AB can be calculated by Euclidean distance formula: distance = sqrt[(x2-x 1)? + (y2-y 1)？ ]。 This formula first calculates the square of the difference between two coordinates, then adds the two square values, and finally takes the square root of this sum. The result is the linear distance between point A and point B. ..
In three-dimensional space, if there are two points A(x 1, y 1, z 1) and B(x2, y2, z2), the distance of AB can be calculated by a similar formula: distance = sqrt[(x2-x 1)? + (y2-y 1)？ + (z2-z 1)？ ]。 This formula is similar to the formula of two-dimensional space, except that the square of one-dimensional difference is added, then the three square values are added, and finally the square root of this sum is taken. The result is the linear distance between point A and point B. ..
These formulas are based on the definition of Euclidean distance, that is, the straight line distance between two points. For other types of distances, such as Manhattan distance or Chebyshev distance, the formula may be different.
In addition, these formulas are only suitable for calculating the straight line distance between two points. If there are curves or polylines between two points, you need to use other methods to calculate the distance. For example, if there is a curve between two points, calculus or other numerical methods can be used to calculate the average of the distances from each point on the curve to the nearest point on the curve as the distance of the curve segment.
The benefits of mathematics:
1. Cultivate logical thinking ability: Mathematics is a subject that needs logical reasoning and can help people cultivate logical thinking ability. Learning mathematics can help people learn how to analyze problems, draw conclusions and solve problems. This ability is very useful in daily life and work, and can help people to deal with all kinds of affairs better.
2. Enhance spatial thinking ability: Geometry and spatial imagination in mathematics are very helpful to enhance spatial thinking ability. This ability can help people better understand the relationship between shape, distance and position in three-dimensional space, which is very important for architecture, art and engineering.
3. Promote the study of other disciplines: Mathematics is a basic discipline, which is of great help to the study of many other disciplines. For example, physics, chemistry, economics and computers all need a certain mathematical foundation. Learning mathematics well can lay a solid foundation for learning other subjects.
4. Enhance the ability to solve problems: Mathematical problems usually require the ability to innovate and solve problems. Learning mathematics can help people learn how to find solutions to problems and how to apply mathematical knowledge to solve practical problems. This ability is very helpful to work and life, and can make people better cope with various challenges.