Maurer rose
Introduction 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.A Maurer rose with ''n'' = 7 and ''d'' = 29
Definition Let ''r'' = sin(''nθ'') be a rose in the polar coordinate system, where ''n'' is a positive integer. The rose has ''n'' petals if ''n'' is odd, and 2''n'' petals if ''n'' is even.We then take 361 points on the rose:: (sin(''nk''), ''k'') (''k'' = 0, ''d'', 2''d'', 3''d'', ..., 360''d''),where ''d'' is a positive integer and the angles are in degrees, not radians.
Explanation A '''Maurer rose''' of the rose ''r'' = sin(''nθ'') 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, (0, 0), and walks along a line to the point (sin(''nd''), ''d''). Then, in the second leg of the journey, the walker walks along a line to the next point, (sin(''n''·2''d''), 2''d''), and so on. Finally, in the final leg of the journey, the walker walks along a line, from (sin(''n''·359''d''), 359''d'') to the ending point, (sin(''n''·360''d''), 360''d''). The whole route is the Maurer rose of the rose ''r'' = sin(''nθ''). A Maurer rose is a closed curve since the starting point, (0, 0) and the ending point, (sin(''n''·360''d''), 360''d''), coincide.The following figure shows the evolution of a Maurer rose (''n'' = 2, ''d'' = 29°).750px
Images The following are some Maurer roses drawn with some values for n and d:750px
Example implementation Using Python:import math, turtlescreen = turtle.Screen()screen.setup(width=800, height=800, startx=0, starty=0)screen.bgcolor('black')pen = turtle.Turtle()pen.speed(20)n = 5d = 97pen.color('blue')pen.pensize(0.5)for theta in range(361):    k = theta * d * math.pi / 180    r = 300 * math.sin(n * k)    x = r * math.cos(k)    y = r * math.sin(k)    pen.goto(x, y)pen.color('red')pen.pensize(4)for theta in range(361):    k = theta * math.pi / 180    r = 300 * math.sin(n * k)    x = r * math.cos(k)    y = r * math.sin(k)    pen.goto(x, y)
References **  (Interactive Demonstrations)
External links Interactive Demonstration: https://codepen.io/Igor_Konovalov/full/ZJwPQv/Explorer: https://filip26.github.io/maurer-rose-explorer/  source codeDraw from values and create vector graphics: https://www.sqrt.ch/Buch/Maurer/maurerroses.html