• 1 Free Group of Rotations ▶
    • 1.1 Selection of Rotations and Decomposition of the Majority of the Sphere
  • 2 Doubling a Sphere ▶
    • 2.1 Sphere
    • 2.2 Duplicating a Part of the Unit Sphere
    • 2.3 Fixed Points and the Center
    • 2.4 The Final Proof
  • Dependency graph

Banach Tarski

Bergschaf

  • 1 Free Group of Rotations
    • 1.1 Selection of Rotations and Decomposition of the Majority of the Sphere
  • 2 Doubling a Sphere
    • 2.1 Sphere
    • 2.2 Duplicating a Part of the Unit Sphere
    • 2.3 Fixed Points and the Center
    • 2.4 The Final Proof