From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Ancient Number Systems (Was: why is pi irrational)
Date: 22 Jan 93 00:28:27 GMT
Organization: Lehigh University

In article <VICTOR.93Jan21101856@terse.watson.ibm.com>,
victor@watson.ibm.com (Victor Miller) writes:
>>>>>> On 20 Jan 93 20:57:08 +1200, pete@bignode.equinox.gen.nz (Pete
Moore) said:
>Pete> Frederick W. Chapman (fc03@ns1.cc.lehigh.edu) wrote:
>Frederick> Actually, the Biblical passage merely describes a circular shaped
>Frederick> pool, saying that it was 30 cubits around and 10 cubits
>Frederick> across (if memory serves me).  This is a far cry from
>Frederick> saying that "pi = 3", for the following reasons. [...]
> ......................................................................
>Pete> The relevant passage is 1 Kings 7 v 23, if anyone cares.
>
>Pete> The `King James' Bible says:
>
>Pete> "...ten cubits from one brim to the other: it was round all
>Pete> about...and a line of thirty cubits did compass it round about."
>
>Pete> and the `Revised Standard Version' varies only in saying "from brim to
>Pete> brim" and "a line of thirty cubits measured its circumference."
> ......................................................................
>It always helps to go back to the original Hebrew.  In the original
>Hebrew, the word for circumference is "Qav", normally spelled qof vav.
>However, in this passage it is spelled qof vav heh.  The Vilna Gaon
>(Rabbi Elijah of Vilna -- probably the leading Jewish religious
>scholar of his day -- in the 18th century, and up to the present day)
>was an avid amateur mathematician: One is forbidden to study religious
>subjects while in the outhouse -- so he studied mathematics there.  He
>commented that the numerical equivalent of qof vav heh is 111 (the
>standard numerics of the Hebrew alphabet give qof = 100, vav = 6 and
>heh = 5), of of qof vav is 106.  If one looks at 3*(111/106) it gives
>pi to four decimal place accuracy!  This would certainly seem to be at
>the limit of the technology of measurement of the day (i.e. King
>Solomon's day).
...........................................................................

This is very impressive!  *proudly bestows the sci.math Biblical
Scholarship Award upon Victor Miller*  :-)

I've heard that letters of the Hebrew alphabet all have numerical
equivalents, which were used in ancient scriptures as the basis of a number
system.  I would be interested in knowing more about this, since it must
surely qualify as a very early example of a number system.  Doesn't some
ambiguity occasionally arise as to whether a given string of characters
should be interpreted as a word or as a numerical quantity?  

Didn't classical Greek also assign numerical values to the letters of the
alphabet and employ a similar number system?  (For example, there is a New
Testament passage that speaks of "the *number* of his name" in reference to
the anti-Christ.)

Thanks,

Fred Chapman
Student of Ancient Number Systems in Religious Writings
:-)>>>
-- 

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