Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-29T23:07:49.682Z Has data issue: false hasContentIssue false
  • English
  • Français

Sums of powers of integers – how Fermat may have found them

Published online by Cambridge University Press:  23 January 2015

Bob Burn
Bob Burn*
Affiliation:
Sunnyside, Barrack Road, Exeter EX2 6AB, e-mail:R.P.Burn@exeter.ac.uk
Get access Rights & Permissions [Opens in a new window]

Extract

On 22 September 1636, Fermat wrote to Roberval, [I, FO.II.XIII, p.71], saying that he had found the quadrature of an infinite number of curves. He named in particular the ‘solid parabola’, y = x3, and said that his method was different from Archimedes‘ quadrature of the parabola. He invited Roberval to share his thoughts on this and other matters.

On 11th October 1636, Roberval replied to Fermat [1. FO.II.XIV, p.75], indicating his method for determining the quadrature of the ‘solid parabola’ and extending it to the quadrature of y = x4 and y = x5.

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 529 , March 2010 , pp. 18 - 26
Copyright
Copyright © The Mathematical Association 2010

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. Tannery, P. and Henry, C., (eds), Oeuvres de Fermat, vol. 2, Correspondance, Gauthier-Villars, Paris (reprinted by Michigan University Press) (1894). References to this book are denoted by FO.II followed by the number of the letter.Google Scholar
2. Mahoney, M. S., The mathematical career of Pierre de Fermat (2nd edn.), Princeton University Press (1994).Google Scholar
3. Edwards, A. W. F., Pascal's arithmetical triangle, Oxford University Press (1987).Google Scholar
4. Fibonacci, Leonardo Pisano, 1225, Liber quadratorum. English translation by Sigler, L. E., The book of squares, Academic Press (1987).Google Scholar
5. Conway, J. H. and Guy, R. K., The book of numbers, Springer Verlag (1996).Google Scholar
6. Bachet, C. G., Diophanti Alexandrini arithmeticorum libri sex, et De numeris multangulis liber unus, Meziriaco Sebusiano, Paris (1621).Google Scholar
7. Beery, J. and Stedall, J., Thomas Harriot's doctrine of triangular numbers: the ‘Magisteria Magna’, European Mathematical Society (2009).Google Scholar
8. Wallis, J., Arithmetica infinitorum, Oxford (1656). English translation by Stedall, J., The arithmetic of infinitesimals, Springer (2004).Google Scholar