Archimedes (bryozoan) Archimedes (bryozoan) Archimedes is a genus of bryozoans belonging to the family Fenestellidae. The first use of the term "Archimedes" in relation to this genus was in 1838. This genus of bryozoans is named "Archimedes" because of its corkscrew shape, in analogy to the Archimedes' screw, a type of water pump which inspired modern ship propellers. These forms are pretty common as fossils but they have been extinct since the Permian. These bryozoans lived from the Carboniferous period (Tournaisian age) to the Permian period (Leonard age) (345.3 to 268.0 Ma), when this genus became extinct. "Archimedes" is a genus of
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