Type 1.
Equations of the Circles:
(x + a(1 - p^ceil(k/2)))² + (y + b(1 - p^floor(k/2)))² = d^k
a = (1 - r)/(1 + r²)
b = r(1 - r)/(1 + r²)
d = r²
p = -r²
0 < r < 1
k = 0, 1, 2, 3, ....
Type 2.
Equations of the Circles:
(x + a(1 - p^floor(k/2)))² + (y + b(1 - p^ceil(k/2)))² = d(1 - r^(k+1))²
a = r²/(1 + r²)
b = r/(1 + r²)
d = (1/(1-r))²
p = -r²
0 < r < 1
k = 0, 1, 2, 3, ....
Type 3.
Equations of the Circles:
(See the equations for Type 1 and Type 2.)
( Mathematical software used: Graph )
Related posts:
- Infinite Families of Tangent Circles (1)
- Infinite Families of Tangent Circles (2)
- Infinite Families of Concentric Circles (1)
- Infinite Families of Concentric Circles (2)
