Friday, December 6, 2013

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 )

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