Maurer rose


In geometry, the concept of a Maurer rose was introduced by Peter M. Maurer in his article titled A Rose is a Rose.... A Maurer rose consists of some lines that connect some points on a rose curve.
[Image:Maurer Rose (n=7,d=29).svg|thumb|300px|A Maurer rose with n = 7 and d = 29]

Definition

Let r = sin be a rose in the polar coordinate system, where n is a positive integer. The rose has n petals if n is odd, and 2n petals if n is even.
We then take 361 points on the rose:
where d is a positive integer and the angles are in degrees, not radians.

Explanation

A Maurer rose of the rose r = sin consists of the 360 lines successively connecting the above 361 points. Thus a Maurer rose is a polygonal curve with vertices on a rose.
A Maurer rose can be described as a closed route in the polar plane. A walker starts a journey from the origin,, and walks along a line to the point. Then, in the second leg of the journey, the walker walks along a line to the next point,, and so on. Finally, in the final leg of the journey, the walker walks along a line, from to the ending point,. The whole route is the Maurer rose of the rose r = sin. A Maurer rose is a closed curve since the starting point, and the ending point,, coincide.
The following figure shows the evolution of a Maurer rose.
750px

Images

The following are some Maurer roses drawn with some values for n and d:
750px

Example implementation

Using Python:

import math, turtle
screen = turtle.Screen
screen.setup
screen.bgcolor
pen = turtle.Turtle
pen.speed
n = 5
d = 97
pen.color
pen.pensize
for theta in range:
k = theta * d * math.pi / 180
r = 300 * math.sin
x = r * math.cos
y = r * math.sin
pen.goto
pen.color
pen.pensize
for theta in range:
k = theta * math.pi / 180
r = 300 * math.sin
x = r * math.cos
y = r * math.sin
pen.goto