Jerzy Kocik
Abstract
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A remarkably simple Diophantine quadratic equation is known to generate all, Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on inversive geometry. Also, occurrence of Pythagorean triples in such gaskets is discussed.
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A remarkably simple Diophantine quadratic equation is known to generate all, Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on inversive geometry. Also, occurrence of Pythagorean triples in such gaskets is discussed.
Key concepts: Diophantine equation, Gasket, Pythagorean triple, Simple (philosophy), Pythagorean theorem, Quadratic equation, Mathematics, Integral equation