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.
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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.
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 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.
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·2d), 2d), and so on. Finally, in the final leg of the journey, the walker walks along a line, from (sin(n·359d), 359d) to the ending point, (sin(n·360d), 360d). 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·360d), 360d), coincide.
The following figure shows the evolution of a Maurer rose (n = 2, d = 29°).
The following are some Maurer roses drawn with some values for n and d:
Using Python:
importmath,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)forthetainrange(361):k=theta*d*math.pi/180r=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)forthetainrange(361):k=theta*math.pi/180r=300*math.sin(n*k)x=r*math.cos(k)y=r*math.sin(k)pen.goto(x,y)
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Interactive Demonstration: https://codepen.io/Igor_Konovalov/full/ZJwPQv/
Explorer: https://filip26.github.io/maurer-rose-explorer/ [source code]
Draw from values and create vector graphics: https://www.sqrt.ch/Buch/Maurer/maurerroses.html