Limaçon as a Roulette - 1

In geometry, a [i]Limaçon[/i], also known as a [i]Limaçon of Pascal[/i], is defined as the roulette formed when a circle rolls around the outside of a circle of equal radius.[br]The red circle [math]c_1[/math] is the fixed circle. The circle [math]c_2[/math] can be rolled around [math]c_1[/math] by moving slider [math]α[/math]. If the common radius of the circles is [math]r[/math], point [math]M[/math] is defined as a point on a distance [math]dr[/math] from[math] O_2[/math]. We can change the position of point [math]M[/math] by moving the slider [math]d[/math]. [br]As the circle [math]c2[/math] rolls around [math]c_1[/math], the point [math]M[/math] will draw the roulette of the circle - the Limaçon. [br][br][list][br][*]Move [math]d [/math] to values less than [math]1[/math], equal to [math]1[/math] or greater than [math]1[/math] to see the change in the Limaçon.[br][/list][br][i]Technical instructions:[/i] Click the "play" button at the lower left corner of the drawing window to start the animation. Click the "reset constructions" button in the upper right to clear the trace marks. Right-click point M to turn tracing on or off.
Limaçon as a Roulette - 1

Information: Limaçon as a Roulette - 1