Archimedes' screw the outer casing to turn the entire apparatus as one piece, which would require that the casing be rigidly attached to the screw. Some researchers have postulated this as being the device used to irrigate the Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World. A cuneiform inscription of Assyrian King Sennacherib (704–681 BC) has been interpreted by Stephanie Dalley to describe casting water screws in bronze some 350 years earlier. This is consistent with classical author Strabo, who describes the Hanging Gardens as irrigated by screws. German engineer Konrad Kyeser equipped the Archimedes screw with
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",