Generalization of the pedal concept in bidimensional spaces. Application to the limaçon of Pascal.

The concept of a pedal curve is used in geometry as a generation method for a multitude of curves. The definition of a pedal curve is linked to the concept of minimal distance. However, an interesting distinction can be made for ℝ². In this space, the pedal curve of another curve C is defined as the locus of the foot of the perpendicular from the pedal point P to the tangent to the curve. This allows the generalization of the definition of the pedal curve for any given angle that is not 90°. In this paper, we use the generalization of the pedal curve to describe a different method to generate a limaçon of Pascal, which can be seen as a singular case of the locus generation method and is not well described in the literature. Some additional properties that can be deduced from these definitions are also described. [ABSTRACT FROM AUTHOR]