The Banach–Tarski paradox says that a solid ball can be split into a finite number of pieces, which are then moved and rotated, without bending or stretching, into two identical copies of the original ball. The reassembly needs as few as five pieces, but those pieces are not solid chunks: they are infinite scatterings of points. The result contradicts intuition that rigid motions preserve volume. It works because the pieces have no defined volume, and it depends on the axiom of choice, a principle in set theory that allows constructing such non-measurable sets. A popular version is the pea and the Sun paradox.

Hampi is a UNESCO World Heritage Site in Karnataka, India, with more than 1,600 surviving remains spread over 4,100 hectares. It was the capital of the Vijayanagara Empire from 1336 to 1565. Travellers from Persia and Portugal described it as a prosperous, wealthy and grand city with temples, markets and farms along the Tungabhadra River. By 1500 it was estimated to be the world's second-largest city after Beijing, and probably India's richest at the time. In 1565 a coalition of Muslim sultanates defeated the Vijayanagara Empire, its capital was conquered and destroyed, and the city was left in ruins. Hampi remains a religious centre, with the active Virupaksha Temple at its heart.