Subject: Re: [HM] Binary Numbers
From: Beatrice Lumpkin (Bealumpkin@aol.com)
Date: Thu Jan 27 2000 - 23:27:22 EST
Dear HM forum members,
On Jan. 25, 2000, Dinesh Maheshwari wrote:
"Recently, I came across a summary of the article by B. van Nooten,
_Binary Numbers in Indian Antiquity_, Journal of Indian Studies,
Volume 21, 1993, pp. 31-50"
The subject was especially interesting to me because I had just returned from
a conference in Thiruvananthapuram, Kerala, India celebrating the 1500th
anniversary of the work of Aryabhata. Two of the papers, presented by members
of the Aryabhata Group, University of Exeter, U.K., were on "Interpreting
Calculus: Evidence for the Transmission from Kerala to Europe." Readers of
George Joseph's "Crest of the Peacock" (see page 289 ff) are aware of the
early development by Kerala mathematicians of elements of calculus including
some work usually attributed to Gregory, Taylor, Leibniz and Newton.
On "binary numbers," in the Rhind Mathematical papyrus (RMP), there are
numerous examples of ancient Egyptian multiplication with successive doubling
of the multiplicand, starting with a multiplier of 1, 2, 4, etc. Then the
powers of 2 whose sum adds to the desired multiplier are checked. The checked
partial products are added, using the distributive property of multiplication
over addition. In effect, the multiplier is converted from a base 10 number
to base 2. In problem 69, for example, to get the multiplier 80, they start
with 1, 2, 4, doubling to 64. Then 16 and 64 are checked, equivalent to
writing 80 in base 2 as 1 0 1 0 0 0 0.
By the way, the Chace translation of the RMP was reprinted by the National
Council of Teachers of Mathematics, 1906 Association Drive, Reston, Virginia
22091. My edition is 1979 but I think it has been reprinted since.
Beatrice Lumpkin
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