Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T07:36:24.198Z Has data issue: false hasContentIssue false
  • English
  • Français

The historical development of complex numbers

Published online by Cambridge University Press:  22 September 2016

D. R. Green
D. R. Green*
Affiliation:
CAMET, University of Technology, Loughborough, Leics. LE11 3TU
Get access Rights & Permissions [Opens in a new window]

Extract

The Alexandrian Greek mathematician Heron—whom we associate with the formula √{s(s − a)(s − b)(s − c)} for the area of a triangle—got involved in a calculation about a pyramid design which led to the evaluation of √(81 − 144). This occurs in his book Stereometria (C. A.D. 75) and to ‘solve’ it the numbers are turned round thus: √(144 − 81), to give √63 which is taken to be . (Is this a reasonable approximation for √63?) It is not known whether Heron made this transpositional error or whether a copier of his work was responsible. This seems to be the first occasion in which the square root of a negative number was stumbled across—a concept not properly understood for another 1750 years!

Type
Research Article
Information
The Mathematical Gazette , Volume 60 , Issue 412 , June 1976 , pp. 99 - 107
Copyright
Copyright © Mathematical Association 1976

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. Smith, D. E., History of mathematics, Vol. 2 (Boston, 1925).Google Scholar
2. Cardano, G., Artis magnae, sive... (the “Ars magna”) (Nuremberg, 1545)Google Scholar
Translated by Witmer, T. R. under the title The great art. M.I.T. Press (1968).Google Scholar
3. Boyer, C. B., A history of mathematics. Wiley (1968).Google Scholar
4. Bombelli, R., L’Algebra (Bologna, 1572).Google Scholar
5. Struik, D. J., A concise history of mathematics. Bell (1954).Google Scholar
6. Hall, T., Carl Friedrich Gauss. A biography. M.I.T. Press (1970).Google Scholar
7. Wilder, R. L., Evolution of mathematical concepts. Wiley (1968).Google Scholar