Dunham, William (1994), The Mathematical Universe (1st ed.), John Wiley and Sons, ISBN 6-3.Dunham, William (1990), Journey Through Genius (1st ed.), John Wiley and Sons, ISBN 0-5.^ "Archimedes' Secret (BBC Documentary)".
A palimpsest stolen from the Greek Orthodox Church in the early 20th century, which reappeared at auction in 1998, contained many of Archimedes works, including The Method of Mechanical Theorems, in which he describes a method to determine volumes which involves balances, centers of mass and infinitesimal slices. His original method likely involved a clever use of levers. It seems that this is not the original method Archimedes used to derive this result, but the best formal argument available to him in the Greek mathematical tradition. Archimedes used an inscribed half-polygon in a semicircle, then rotated both to create a conglomerate of frustums in a sphere, of which he then determined the volume.
The argument Archimedes used to prove the formula for the volume of a ball was rather involved in its geometry, and many modern textbooks have a simplified version using the concept of a limit, which did not exist in Archimedes' time. Later, Roman philosopher Marcus Tullius Cicero discovered the tomb, which had been overgrown by surrounding vegetation. Archimedes was particularly proud of this latter result (as it was allegedly inscribed on his tombstone discovered by Cicero), and so he asked for a sketch of a sphere inscribed in a cylinder to be inscribed on his grave. This result would eventually lead to the Lambert cylindrical equal-area projection,Ī way of mapping the world that accurately represents areas. Is equal to the area of the cylinder minus its caps. Showed that both the volume and the surface area of the sphere were two-thirds that of the cylinder.
Let r, so that the sphere touches the cylinder at the top and bottom, he The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder. Contents The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes
#ABOUT ARCHIMEDES PRINCIPLE HOW TO#
It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so. On the Sphere and Cylinder ( Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a work that was published by Archimedes in two volumes c. Mathematical proofs published by Archimedes A page from "On the Sphere and Cylinder" in Latin
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