question about quadratics

To all the math-geeks:

It's well-established that the Babylonians had
highly developed algebraic methods, altho they
never actually developed an algebraic notation.

There's also concrete proof that they had very good
sexagesimal approximations to both square and cube roots.

I'm investigating the possible applications some
of these methods may have had to tuning problems,
but my extremely math-challenged self needs some help.

Can someone tell me what application quadratic equations
may have to determining string-lengths? I'm interested
in possible applications for the purposes of determining
both JIs and/or temperaments.

For a reference to a modern explanation of Babylonian
algebra, please see the following, p 30-50:

Neugebauer, Otto. 1957.
_The Exact Sciences in Antiquity_.
Providence, Brown University Press, 2d ed
L.O.C.#: QA22 .N36 1957

Thanks.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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This may also be useful / helpful / interesting:

"Pythagorean Triangles and Musical Proportions"
by Martin Euser
http://www.nexusjournal.com/Euser.html

----- Original Message -----
From: monz <joemonz@yahoo.com>
To: <tuning-math@yahoogroups.com>
Sent: Monday, October 22, 2001 11:30 AM
Subject: [tuning-math] question about quadratics

> To all the math-geeks:
>
> It's well-established that the Babylonians had
> highly developed algebraic methods, altho they
> never actually developed an algebraic notation.
>
> There's also concrete proof that they had very good
> sexagesimal approximations to both square and cube roots.
>
> I'm investigating the possible applications some
> of these methods may have had to tuning problems,
> but my extremely math-challenged self needs some help.
>
> Can someone tell me what application quadratic equations
> may have to determining string-lengths? I'm interested
> in possible applications for the purposes of determining
> both JIs and/or temperaments.
>
>
> For a reference to a modern explanation of Babylonian
> algebra, please see the following, p 30-50:
>
> Neugebauer, Otto. 1957.
> _The Exact Sciences in Antiquity_.
> Providence, Brown University Press, 2d ed
> L.O.C.#: QA22 .N36 1957
>
>
> Thanks.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com