Archimedes' screw rivers, including the Thames, powering Windsor Castle. In 2017, the first reverse screw hydropower in the United States opened in Meriden, Connecticut. The Meriden project was built and is operated by New England Hydropower having a nameplate capacity of 193 kW and a capacity factor of approximately 55% over a 5-year running period. Archimedes' screw An Archimedes' screw, also known by the name the Archimedean screw or screw pump, is a machine used for transferring water from a low-lying body of water into irrigation ditches. Water is pumped by turning a screw-shaped surface inside a pipe. The screw pump is
Archimedes Palimpsest a parabola and one of its secant lines. (For explicit details, see Archimedes' use of infinitesimals.) When rigorously proving theorems, Archimedes often used what are now called Riemann sums. In "On the Sphere and Cylinder," he gives upper and lower bounds for the surface area of a sphere by cutting the sphere into sections of equal width. He then bounds the area of each section by the area of an inscribed and circumscribed cone, which he proves have a larger and smaller area correspondingly. He adds the areas of the cones, which is a type of Riemann sum for the