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Topic: [HM] Heron's Stereometrica
Replies: 3   Last Post: Feb 23, 2001 2:47 PM

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Antreas P. Hatzipolakis

Posts: 940
Registered: 12/3/04
Re: [HM] Heron's Stereometrica
Posted: Feb 22, 2001 6:03 PM
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Andre Gevisier wrote:

> Somewhere it was said that the first instance of a problem leading
> to an imaginary number is in Stereometrica, by Heron of Alexandria.
> Does anyone have access to that book and is able to give me some
> more information about the problem in question?

Quoting Ed Sandifer's review of the book:
_An Imaginary Tale: The Story Of Sqrt(-1)_ by Paul J. Nahim.

The book follows a roughly historical trail, opening with a story of how
ancient mathematicians Heron and Diophantus missed a chance to discover
imaginary numbers. Both knew a formula for the volume of a truncated
square pyramid in terms of the sides of the upper and lower square
surfaces and the length of the edge connecting those sides. In one of his
examples, Heron picked a length, 15, for the edge that wasn't long enough
to reach the corners of the squares, of sides 28 and 4. Perhaps he was
teaching too many classes that semester, for when Heron reached a point
where he was to take the square root of a negative value, he just took the
root of a positive instead, and thus missed a chance to discover imaginary
numbers. It took over a thousand years until del Ferro and Cardano actually
made the discovery in their pursuit of roots of cubic equations. Nahin
tells this familiar story with delightful enthusiasm.


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