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Several experiments were carried out including a large scale test with 500 schoolchildren aiming mirrors at a mock-up of a Roman sailing ship 400 feet (120 m) away. A coating of tar would have been commonplace on ships in the classical era. In all of the experiments the sail failed to reach the 210 °C (410 °F) required to catch fire and the verdict was again "busted".
He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series and gave a remarkably accurate approximation of pi. He is credited with designing innovative machines including siege engines and the screw pump that bears his name. He also defined the spiral bearing his name formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
