Yin Yang 4
| One of the many celtic motifs is familiar with four Yin Yang symbols. Drawing this symbol with compass and ruler is fun, but there is also algebra involved. There are only two parameters: the size of the circle and the width of the band. Say OA=1, the width of the band AE = AM is limited. It can be almost zero, but it is always less than one. | |
Exercise 0
Draw this celtic symbol with compass and ruler.
Exercise 1
Key characteristic of this motif is the width of the black and the white band.
Point is at line . The closer point is to point the larger the drops and the smaller the width of the band. The closer to point , the smaller the drops and the larger the width of the band.
Say . Proof that:
- the exact values of the limiting values of the position of point on line are and .
- the maximum width of the white and the black band is
Exercise 2
Say that and that the radius of the greater circle is and that the radius of the smaller circle is and that the width of the band is . Proof that