Paderborn

Paderborn begins with water and empire. The Pader, Germany's shortest river, springs from some two hundred warm sources directly beneath the cathedral quarter and runs barely four kilometres — a river born and finished within one city, its pools steaming gently in winter. Above the springs Charlemagne built a palace, and in 799 received Pope Leo III here: the meeting that arranged the imperial coronation of 800 — Europe's medieval order was sketched, in effect, beside the Pader's sources, and the excavated Carolingian palace beside the cathedral museum tells the story on the spot.

The cathedral's treasury ranks with Germany's richest, and its cloister window holds the town's beloved riddle: the Three Hares Window, three hares sharing three ears yet each possessing two — a medieval trick of geometry adopted as Paderborn's emblem. Each July the city erupts in Libori, nine days of fairground, processions and concerts around the relics of St Liborius — one of Germany's oldest and largest town festivals, sealed by a 1,200-year-old friendship pact with Le Mans.

The modern city added an unexpected superlative: the Heinz Nixdorf MuseumsForum, the world's largest computer museum, ciphers to smartphones across two exhibition floors — fitting for a university city strong in informatics. Charlemagne's springs, three impossible hares and the history of the machine: Paderborn's portfolio spans the whole millennium and change.