engleski

Playing with the Constructions of Limacon

The Limacon of Pascal is a well studied curve of the fourth order. We know a lot about its properties and a number of ways to construct it. For instance, Limacon is a pedal curve of a circle, an inverse of a conic when the center of the ordinary circle inversion is the focus of the conic, or an envelope of circles through a given point with the centers on a given circle. Furthermore, due to different ways of construction, the Limacon belongs to several types of curves or is a special type of some other plane curve. It can be constructed as a conchoid of a circle or it can be defi ned as an epicycloid, i.e., a roulette formed by the path of a point fi xed to a circle when that circle rolls around a circle. In this presentation we will talk about curves obtained by constructions similar to those of the Limacon, but changing some basic elements of the constructions. For an example, let say that, in the construction of Limacon as an envelope of circles, we take that the centers of those circles lie on a given conic and not on a circle.

Limacon, conic, roulette, conchoid

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