User:08glasgow08/Mauesr Rose

Definition

A Maurer rose was introduced by Peter M. Maurer in his article entitled A Rose is a Rose…[1]. A Maurer rose consists of some lines which connect some points on a rose.

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:

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

where d is a positive integer and the angles are in degrees, not radians.

A Maurer rose consists of the 360 lines successively connecting the above 361 points.

Images

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

Maple code

The following is the Maple code for plotting Maurer roses:

with(plots):

n:=7:d:=29:

Rose:=plot(sin(n*t),t=0..2*Pi,coords=polar,thickness=2):

K:=360:

for k from 0 to K do k1:=k*d*Pi/180:k2:=(k+1)*d*Pi/180:

Point[k]:=pointplot([sin(n*k1),k1],coords=polar,color=blue):

Maurer_rose[k]:=listplot([[sin(n*k1),k1],[sin(n*k2),k2]],coords=polar,color=blue):od:

Maurer_rose:=display(seq(Maurer_rose[k],k=0..K)):

Point:=display(seq(Point[k],k=0..K)):

display(Rose,Point,Maurer_rose);

References

1. Peter M. Maurer. A Rose is a Rose.... The American Mathematical Monthly. August-September 1987, Volume 94, Number 7, pp. 631-645 [2]

2. Interactive Demonstrations of Maurer roses