His namesake mean is a weighted average of the arithmetic and geometric means, though a more famous contribution was proven in his Metrica.
Among his inventions were a coin-operated machine that dispensed water for ritual cleansing and a thrysus that whistled when thrust underwater. Before Fermat, he stated the (*)  principle of the shortest path of light, and other notable inventions include steam-powered fire engines and water organs, which were described in his Pneumatica. His namesake mean is a weighted average of the arithmetic and geometric means, though a more famous contribution was proven in his Metrica. For 10 points, name this Alexandrian whose eponymous formula allows one to find the area of a triangle utilizing its semiperimeter given the lengths of its sides.
Among his inventions were a coin-operated machine that dispensed water for ritual cleansing and a thrysus that whistled when thrust underwater.
{Hero}n of Alexandria