Screw (simple machine) of the last of the simple machines to be invented. It first appeared in ancient Greece and Egypt, and by the first century BC was used in the form of the screw press and the Archimedes' screw, but when it was invented is unknown. Greek philosopher Archytas of Tarrentum (428 – 347 BC) was said by the Greeks to have invented the screw. Although the Greek philosopher Archimedes is credited by the Greeks with inventing the Archimedes screw water pump around 234 BC. records indicate it was first used in ancient Egypt. Archimedes was first to study the screw as
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",