Let m be any point on the plane, and the distance between the pole o and the point m |OM| is called the polar diameter of the point m, which is recorded as ρ; ∠xOM takes the polar axis Ox as the starting edge and the ray OM as the ending edge, which is called the polar angle of point M, and is recorded as θ. The ordered number pair (ρ, θ) is called the polar coordinate of point M, and it is denoted as M(ρ, θ).
Newton was the first person to use polar coordinates to determine the position of a point on a plane. His Flow Method and Infinite Series was written in 167 1 and published in 1736. This book includes many applications of analytic geometry, such as drawing curves according to equations. One of the creations in the book is the introduction of a new coordinate system.
Extended data
There are some curves on the plane. When polar coordinates are used, the equation is relatively simple. For example, the polar coordinate equation of a circle with the origin as the center and R as the radius is ρ=r, and the polar coordinate equation of a constant-speed spiral is ρ=aθ. In addition, three different conic curves, ellipse, hyperbola and parabola, can be expressed by a unified polar coordinate equation.
For any point P on the plane, ρ represents the length of the line segment op, which is called the polar diameter or vector diameter of the point P, the included angle θ between ox and op belongs to [0,2π], which is called the polar angle or radial angle of the point P, and the ordered number pair (ρ, θ) is called the polar coordinate of the point P. The polar diameter of the pole is zero and the polar angle is uncertain. Except for the poles, a point has a one-to-one correspondence with its polar coordinates.
Baidu encyclopedia-polar coordinates