Figure 1: Rosettes
Figure 2: Rosettes
Figure 3: Rosette
Figure 4: 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.
- If one allows for rational values, closed curves also result (see Fig. 2).
- The curves are not closed for irrational values of (see Fig. 4).
- 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 .
↑ Pêndulo de Foucault ( Portuguese WP)