The infinite series 1 minus 1 plus 1 minus 1 and so on never settles on a single total, because its partial sums keep bouncing between 1 and 0. Yet mathematicians can assign it a value using summation methods that handle divergent series. Using these methods, the series can be assigned the value one half, and it is named after the Italian priest and mathematician Guido Grandi, who discussed it in 1703. Grandi argued that the sum was one half by grouping terms in pairs and thinking of the series as a shifting pattern. Later, many mathematicians found the result useful in areas like the theory of divergent series. Ordinary addition cannot handle it, but a broader definition of sum can. The series shows how the idea of a sum depends on the rules you choose.

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.