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POPSMath Behind Ancient Islamic Tile Patterns Decoded When Peter J. Lu traveled to Uzbekistan, he had no idea of the mathematical journey that he was about to embark on as well. See the full research article as published in Science . It's a wonderful example of original, multidisciplinary academic research bridging history and mathematics that happens to force us to re-think the sophistication of ancient geometrical knowledge. When Lu looked at photographs of Islamic buildings, he found that he could break the patterns on their surfaces up into the same shapes, even though the shapes often weren't immediately visible. "I couldn't sleep for days," he said. "I skipped Christmas break to work on it."