On a Diophantine Equation That Generates All Integral Apollonian Gaskets

Figure 12

Arrangement (𝑏₀,𝑏₁,𝑏₂,𝑏₃)=(−3,5,8,8) or (𝐵,𝜇,𝑘,𝑛)=(3,4,5,5). Both symbols (left) and Pythagorean triples (right). The triangles are reported with absolute values of sides.