What me know what I m talking about just commiting a bit of original research and shouting history Anyway I did a bit of digging in google which turned up Gregory St Vincent Gr goire de Saint Vincent with The Greeks described a spiral using an angle and a radius vector but it was St Vincent and Cavalieri who simultaneously and independently introduced them as a separate coordinate system In an article The Origin of polar coordinates J J Coolidge refers to the priority dispute between Cavalieri and St Vincent over their discovery St Vincent wrote about this new coordinate system in a letter to Grienberger in 1625 and published the process in 1647 On the other hand Cavalieri s publication appeared in 1635 and the corrected version in 1653 and Milestones in the History of Thematic Cartography Development of the use of polar coordinates for the representation of functions Newton s Method of Fluxions was written about 1671 but not published until 1736 Jacob Bernoulli published a derivation of the idea in 1691 238 p 324 attributes the development of polar coordinates to Fontana with no date Isaac Newton 1643 1727 England and Gregorio Fontana 1735 1803 and Jacob Bernoulli 1654 1705 238 p 324 1671 is probably too early 17361755 would probably be more appropriate There are earlier references to Hipparchus 190 120BC regarding the use of polar coordinates in establishing stellar positions and Abu Arrayhan Muhammad ibn Ahmad al Biruni 1021 regarding the use of three rectangular coordinates to establish a point in space 1843 Use of polar coordinates in a graph frequency of wind directions L on Lalanne 1811 1892 France 148 La Habra High School Math History Timeline Jacob Bernoulli invents polar coordinates a method of describing the location of points in space using angles and distances Sherlock Holmes in Babylon and Other Tales of Mathematical History has a section Newton as an originator of polar coordinates Jacob Amsler Amsler invented the polar planimeter a device for measuring areas enclosed by plane curves It was based on polar coordinates whereas earlier instruments were based on cartesian coordinates In 1856 Amsler published a paper ber das Planimeter in which he gave details of his idea As Mahoney writes in 1 Amsler s planimeter adapted easily to the determination of static and inertial moments and to the coefficients of Fourier series it proved especially useful to shipbuilders and railway engineers So it seems there is considerable different accounts of their introduction and quite a few notable applications