A geometrical figure commonly attributed to Archimedes in 300 BC has been identified in Minoan wall paintings dated to over 1,000 years earlier. The mathematical features of the paintings suggest that the Minoans of the Late Bronze Age, around 1650 BC, had a much more advanced working knowledge of geometry than has previously been recognized, says computer scientist Constantin Papaodysseus of the National Technical University of Athens, Greece, and his colleagues.The paintings appear in a building that is still being excavated and restored in the ancient Minoan town of Akrotiri on the island of Thera. A catastrophic eruption of the volcano on Thera, now known as Santorini, around 1650 BC, is thought to have dealt a fatal blow to the Minoan culture. The blast covered Akrotiri, on the island's southern coast, in a thick layer of ash that preserved many buildings and artefacts.Ten or so buildings have been excavated in Akrotiri so far, including a large one known as Xeste 3, which stands close to the ancient quay. Judging from its large size and extensive wall decorations, Xeste 3 appears to have been some kind of public building, such as a temple or a place for ritual ceremonies.The most impressive feature of the paintings found in Xeste 3 is a series of spirals, each about 32 centimetres in diameter and embellished with dots. Papaodysseus and his team have shown that these are near-perfect Archimedes' spirals: shapes tightly defined by a simple mathematical formula, in which the distance between the windings is constant.Some spirals, such as the ones found on snail shells, are common in nature. And others can be easily made by unwinding a thread around a central peg. But the Archimedes' spiral is not like either of these. "Seemingly it does not exist in nature," the researchers say."This is the earliest time that such advanced geometric figures have been spotted," says Papaodysseus. "The next such figures appear only 1,300 years later." The team report their work in the journal Archaeometry.Papaodysseus and his co-workers admit that they cannot know how much the Theran artists actually understood about the geometric principles they used for the paintings, because no written documents from this period are known to exist.