Special Rose Surfaces

appearance

different colored petals

numerator n

9

8

7

6

5

4

3

2

1

denominator d

1

2

3

4

5

6

7

8

9

In the plane

z=0

, a rose (or rhodonea) is a curve

R(n,d)

, given by the polar equation

r=sin

n

d

φ

, where

n

d

is a positive rational number in lowest terms. This is a directing curve of a special rose surface

SR(n,d)

presented in this Demonstration.

SR(n,d)

is the system of circles with diameters

OR

that are perpendicular to the

z=0

plane, where

O

is the origin and

R≠O

is a point of the rose

R(n,d)

.