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Scientific American ISOPERIMETRY: A conundrum dating back to the ancient Greeks called Dido s problem asks: Among all planar figures having the same perimeter, which one encloses the greatest area? The answer, the Greeks knew, is the circle, and it was finally proved in the 19th century. But a related problem persists in non-Euclidean geometry. Gilles Courtois, director of research at the Institute of Mathematics of Jussieu in France, was studying this question. “We thought that we had found a path toward a solution,” he says. “The scheme was so simple that we were able to write it on the board.” Unfortunately, the idea didn t pan out, and the project “remains a work in progress.” Credit: Jessica Wynne ....