The surface area of the bicylinder and Archimedes' method
type: Item
instance of: scholarly article
title: The surface area of the bicylinder and Archimedes' method
zbMATH Open document ID: 1007.01003
author: Jan P. Hogendijk
published in: Historia Mathematica
publication date: 2002-07-08T00:00:00Z
review text: ``A bicylinder is the intersection of two equal right circular cylinders whose axes intersect at right angles. Archimedes says in his \textit{Method} that the volume of the bicylinder is two-thirds of the volume of the cube whose edge is equal to the diameter of the cylinders. The surface area of the bicylinder is also two-thirds of the surface area of this cube. I argue that this result was known to Archimedes.'' Archimedes mag diesen Satz im letzten Teil seiner \textit{Method}, der verloren ist, bewiesen haben. Der Verfasser beweist den Hilfssatz: Ist \(d\) die Würfelkante, dann ist die Oberfläche 4\(d^2\) des Bizylinders 2/3 der Oberfläche des umschriebenen Würfels: \[ 4 d^2= (2/3)\cdot 6\cdot d^2. \] Mit Hilfe dieses Satzes rekonstruiert der Verfasser den Beweis für die Behauptung des Archimedes.
Mathematics Subject Classification ID: 01A20
zbMATH DE Number: 1764733
Wikidata QID: Q59319696
reviewed by: Johann Jakob Burckhardt
MaRDI profile type: Publication
OpenAlex ID: W2026926247
cites work: Didactical and Other Remarks on Some Theorems of Archimedes and Infinitesimals
cites work: Q3789500
cites work: Q4378681
cites work: A new reading of \textit{Method} proposition 14: Preliminary evidence from the Archimedes Palimpsest. I
cites work: Q4726198
DOI: 10.1006/HMAT.2002.2349
description: scientific article; zbMATH DE number 1764733