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Maurer Rose Pattern


A Maurer rose of the rose r = sin(nθ) consists of the 360 lines successively connecting the mentioned below 361 points, where n is a positive integer. The rose has n petals if n is odd, and 2n petals if n is even.
We take 361 points on the rose as:

(sin(nk), k) (k = 0, d, 2d, 3d, ..., 360d),

where d is a positive integer and the angles are in degrees, not radians. 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).
    A Maurer rose is a closed curve since the starting point, (0, 0) and the ending point, (sin(n·360d), 360d), coincide.



Last update: December 25, 2021