What kind of mathematical equation does that flower contain?

Spring has come and the garden is full of flowers. However, have you found that the distribution of flowers, leaves and branches is very symmetrical, balanced and coordinated: peach blossom and wintersweet, their flowers form a five-petal symmetrical radiation pattern; The arrangement of fruits on the sunflower disk, the division of pineapple fruits and the tillering of winter wheat grow in a symmetrical spiral form in space ... Many flowers not only show the beauty of birth, but also show the beauty of mathematics.

Mathematicians have long noticed that the shapes of leaves and flowers of some plants are very similar to some closed curves.

They use equations to describe the outer contour of flowers. These curves are called "rose lines". Mathematically, there are three-leaf rose lines [equation is ρ = Asin (3β)] and four-leaf rose lines [equation is ρ = Asin (2β)]. The polar coordinate equations of these curves are very simple, and the basic form is: ρ=Asin(nβ), that is, the polar radius ρ of any point is a function of angle β; The rectangular coordinate equation is: x=Asin(nβ)cos(β), y=Asin(nβ)sin(β).

The following are the curve equations of several flowers obtained by scientists through research.

The equation of jasmine petals is:

The equation of clover is ρ=4( 1+cos3φ+3sin23φ sunflower line equation is:

θ θ beautiful "recent love" equation curve;

Butterfly function: ρ = 0.2 sin (3 θ)+sin (4 θ)+2 sin (5 θ)+1.9 sin (7 θ)-0.2 sin (9 θ)+sin (11θ flower function: ρ = 3 sin (.