Take a fixed point O on the plane, which is called the pole, draw a ray Ox, which is called the polar axis, and then choose a length unit and the positive direction of the angle (usually counterclockwise). For any point m on the plane, ρ represents the length of the line segment om, θ represents the included angle between Ox and OM, ρ is the polar diameter of point M, θ is the polar angle of point M, and the ordered number pairs (ρ, θ) are the polar coordinates of point M..

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 innovations in the book is the introduction of a new coordinate system .40438+07 or even 6536. Its y value is plotted in the direction perpendicular or oblique to the x axis. One of the coordinates introduced by Newton is based on a fixed point and a straight line passing through this point, just like our current polar coordinate system. Newton also introduced bipolar coordinates, in which the position of each point depends on its distance from two fixed points. Because Newton's work was not discovered until 1736, but the Swiss mathematician J. Bernoulli published an article about polar coordinates in 169 1 year in Teachers' Magazine, so J. Bernoulli is generally regarded as the discoverer of polar coordinates. J. Herman, a student of J. Bernoulli, not only officially announced the universal availability of polar coordinates in 1729, but also freely used polar coordinates to study curves. He also gave the conversion formula from rectangular coordinates to polar coordinates. To be exact, J. Herman took cos and sin as variables and expressed them by Z, N and M. Euler of Cos and sin expanded the application range of polar coordinates and explicitly used the symbols of trigonometric functions. Euler's polar coordinate system at that time was actually a modern polar coordinate system.

Using polar coordinate method to deal with some geometric trajectory problems, its equation is simpler than rectangular coordinate method, and drawing is more convenient. In 1964, J. Bernoulli introduced lemniscate with polar coordinates, and this curve played a considerable role in18th century.