[b][url=https://en.wikipedia.org/wiki/Polar_coordinate_system]The polar coordinate system[/url][/b] is a [url=https://en.wikipedia.org/wiki/Dimension]two-dimensional[/url] [url=https://en.wikipedia.org/wiki/Coordinate_system]coordinate system[/url] in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.[br][br][size=150]Converting between Polar and Cartesian coordinates:[/size][br][img width=250,height=248]https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Polar_to_cartesian.svg/250px-Polar_to_cartesian.svg.png[/img][br][img]https://wikimedia.org/api/rest_v1/media/math/render/svg/32c7f6c81b7b59f338ab20da873bdd8e714f347b[/img][br][br][size=150]Task: [/size][br]The curve is given by polar equation r = 2+2cos [b]φ[/b]. Determine the point with minimal curvature.[br][br]First, rewrite polar coordinates to the cartesian coordinates. Instead of the greek letter [b]φ[/b], we can use the letter [i]t[/i].[br]x = (2+2cos t).cos t[br]y = (2+2cos t).sin t

Start the animation of revolving parameter a (left down corner). Value of slider u specify the position of osculating circle (red).

Stop the animation and set up the trace on for osculating circle. Then change the value of parameter u on red slider.