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Hero and Theon connected by matrices

Published online by Cambridge University Press:  03 November 2016

L. E. Ellis
L. E. Ellis*
Affiliation:
Marlborough College, Marlborough, Wiltshire
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Extract

In a course on Greek Mathematics for our Classical Sixth some years ago, I noticed a connection between Theon’s and Hero’s sequences of rational approximations to √2 (the “side-and-diameter” numbers). A footnote in Heath [1] refers to a proof published in German in 1886, but I recently came across a generalisation which may be of some interest.

Type
Research Article
Information
The Mathematical Gazette , Volume 58 , Issue 404 , June 1974 , pp. 135 - 137
Copyright
Copyright © Mathematical Association 1974

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References

1. Heath, T. L., A history of Greek mathematics. Oxford University Press (1921).Google Scholar
2. Davenport, H., The higher arithmetic. Hutchinson (1952).Google Scholar
3. T. J. Fletcher, , Linear algebra through its applications. Van Nostrana Reinhold (1972).Google Scholar