Polar coordinate意思
"Polar coordinate" is a term used in mathematics, particularly in geometry and calculus, to describe a system for identifying points on a plane. Unlike the more familiar Cartesian coordinate system, which uses two perpendicular axes (the x-axis and y-axis) to specify points using two coordinates (x, y), the polar coordinate system uses a central point (like the center of a circle) and a ray (also called an initial or polar axis) that extends from this central point.
In a polar coordinate system, each point is identified by two pieces of information:
- The radial distance (r) from the central point to the point on the plane.
- The angle (θ), measured in radians or degrees, from a reference direction (often the positive x-axis or the 1st quadrant) to the ray connecting the central point to the point on the plane.
So, a point in a polar coordinate system is denoted by (r, θ), where r is the radial distance and θ is the angle. The angle is measured counterclockwise from the reference direction.
Polar coordinates are particularly useful for describing shapes and movements that are naturally described in terms of angles and distances, such as the path of a projectile or the shape of a circle or an ellipse. They are also used in complex analysis and in some branches of physics, such as electromagnetism and quantum mechanics.