Rosette (curve)

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Figure 1: Rosettes
Figure 2: Rosettes
Figure 3: Rosette
Figure 5: Rosettes

In geometry, a rosette is a plane curve that is expressed in polar coordinates by an equation

can be described, d. H. the associated parametric representation is



is the circle with the equation ,
is a quadrifolium (4-leaf rosette),
is a trifolium (3-leaf rosette),
there is an 8-petalled rosette,
there is a 5-petalled rosette.


the rosette is straight- leaved.
the rosette is odd - leaved.

Note: Using the sine function instead of the cosine function only rotates the rosette.

  1. If one allows for rational values, closed curves also result (see Fig. 2).
  2. The curves are not closed for irrational values ​​of (see Fig. 4).
  3. Adding to a constant: results in rosettes with large and small petals (see Fig. 3).

Note: The Foucault pendulum describes an open rosette curve.


A rosette has the area

if n is even, and

if n is odd.

So there is a simple relationship with the area of ​​the surrounding circle with radius .

Web links

Individual evidence

  1. Pêndulo de Foucault ( Portuguese WP)