Infinite Families of Tangent Circles (3) (無限相切圓系 3)

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)