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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
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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

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References

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