Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T15:01:11.677Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalisation of Archimedes' method

Published online by Cambridge University Press:  23 January 2015

Christoph Kirfel
Christoph Kirfel*
Affiliation:
Department of Mathematics, Johannes Brunsgt, 12, 50 20 Bergen, Norway, e-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Archimedes developed a method for calculating the area of a segment of a parabola. This result was outstanding in mathematical antiquity. The idea and the method were not developed further until nearly 1800 years later. In our article his method is presented in modem notation using modem concepts. We show that the method generalises to curves of higher order. Many of Archimedes' arguments can be used without any adjustments and thus show the strength of his original approach.

The mathematician from Syracuse, Archimedes (born about 287 BC, died 212 BC), developed a method for the calculation of the area of a segment of the parabola.

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 538 , March 2013 , pp. 43 - 52
Copyright
Copyright © The Mathematical Association 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Eves, H., An Introduction to the History of Mathematics (5th edn.), Saunders College Publishing (1983).Google Scholar
2. Burn, R. P., Integration, a genetic introduction, Nordisk matematikk didaktikk, Vol. 7, Nr. 1, (April 1999).Google Scholar
3. Toeplitz, O., Die Entwicklung der Infinitesimalrechnung, Springer (1949).Google Scholar
4. http://www.math.ubc.ca/~cass/archimedes/parabola.html Google Scholar
5. http://www.claymath.org/library/historical/euclid/ Google Scholar
6. http://alephO.clarku.edu/~djoyce/java/elements/elements.html Google Scholar