Archimedes' screw the screw and casing could be cast together as a single piece in bronze. The design of the everyday Greek and Roman water screw, in contrast to the heavy bronze device of Sennacherib, with its problematic drive chains, has a powerful simplicity. A double or triple helix was built of wood strips (or occasionally bronze sheeting) around a heavy wooden pole. A cylinder was built around the helices using long, narrow boards fastened to their periphery and waterproofed with pitch. The screw was used predominately for the transport of water to irrigation systems and for dewatering mines or other low-lying
Archimedes' quadruplets theorem: Also: Combining these gives: Expanding, collecting to one side, and factoring: Solving for "x": Proving that each of the Archimedes' quadruplets' areas is equal to each of Archimedes' twin circles' areas. Archimedes' quadruplets In geometry, Archimedes' quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making them Archimedean circles. An arbelos is formed from three collinear points "A", "B", and "C", by the three semicircles with diameters "AB", "AC", and "BC". Let the two smaller circles have radii "r" and "r",