This interactive simulation visualizes the Banach-Tarski Paradox, where a solid sphere can be split into a finite number of non-overlapping pieces and reassembled into two identical copies of the original sphere.

Observe the decomposition of the sphere into fragments and watch as they reassemble into two identical spheres, demonstrating the paradox.

The continuous version of the Banach-Tarski Paradox demonstrates a smooth transformation where a sphere gradually splits into two identical spheres through an infinite process of rotations and movements. This visualization allows you to explore the paradox in a dynamic and continuous manner.

Click the 'Continuous Visualization' button to observe the continuous transformation and delve deeper into the fascinating concepts of infinity and geometry.

• Click the 'Split and Reassemble' button to initiate the simulation.
• Use the control panel to adjust visual settings such as background, shading, and shadows.
• Rotate and zoom the model using your mouse for different perspectives.
• Click the 'Continuous Visualization' button to see the continuous version of the paradox.
• Click 'Split and Reassemble' again to split the reassembled spheres further.