[1313] Mathematical Problem

Guest poem submitted by David McKelvie,
<david@>:

Whilst making love a necklace broke.
A row of pearls mislaid.
One sixth fell to the floor.
One fifth upon the bed.
The young woman saved one third of them.
One tenth were caught by her lover.
If six pearls remained upon the string
How many pearls were there altogether?

	-- Bhaskaracharya

In a previous life I studied mathematics at university. Before I even
started my studies, I had always felt that there was a connection
between a mathematical proof and a poem. Usually, both are divided into
lines. They tell "truths" (though in both maths and poetry, these may
sometimes be paradoxical, nonsensical even).  The best ones have an
indescribable beauty and inevitability to them. They are a product of an
individual mind, intent on searching for something and finding it.

It was with some pleasure then, a year into my studies, that I
discovered classic Indian mathematics. Indian mathematicians essentially
invented modern mathematics in the first millenium: they created our
place value system; discovered the zero we use today as a number and a
concept; were the first people to create a mathematical definition of
infinity; and they wrote virtually all of their mathematical works in
verse.

I found this problem-poem in a book called The Universal History of
Numbers by Georges Ifrah. In it he says: "Numerical tables, Indian
astronomical and mathematical texts, as well as mystical, theological,
legendary and cosmological works were nearly always written in verse...
From this type of game, the Indian scholars went on to use imagery to
express numbers; the choice of synonyms [for whole numbers] was almost
infinite and these were used in keeping with the rules of Sanskrit
versification to achieve the required effect. Thus the transcription of
a numerical table or of the most arid of mathematical formulae resembled
an epic poem."

This poem was originally written in 1150 by Bhaskaracharya, a
mathematician and mechanic and is taken from a book he wrote called the
Lilavati, filled with poetic mathematical problems.

The most appealing thing I find about it, is that it takes a simple
algebraic problem and dresses it up in a lovely little human drama:
falling pearls interrupting a lover's embrace. Maths was never presented
hand in hand with lovemaking when I studied it! {And the answer is
fairly easy to get... try it! It's not hard!}

David.

[Minstrels Links]

Poem #599, Geometry  -- Rita Dove
Poem #601, Hall and Knight -- E. V. Rieu
Poem #604, Euclid Alone Has Looked On Beauty Bare -- Edna St. Vincent
Millay
Poem #797, Big Whirls Have Little Whorls -- Lewis F. Richardson
Poem #805, Rigid Body Sings -- James Maxwell
Poem #1205, Love and Tensor Algebra -- Stanislaw Lem

[this poem is archived, accessible and awaiting your comments at]
http://www.cs.rice.edu/~ssiyer/minstrels/poems/1313.html
To subscribe, send a blank mail to <minstrels-subscribe@>.

From: Anil Menon <anilm411@>

Minor attribution note: The poem is derived from the
Manoranjana, a commentary on the Lilavati, written by
Rama Krishna Deva [period uncertain]. It appears as an
additional problem attached to stanza 54, Chapter 3.
See the footnote on page 33 of Colebrooke's
translation of Lilavati (Asian Education Services,
1993, 2nd Edition, with notes by H. C. Banerji). 

Pedantically,

--Anil Menon   





		
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From: Wizkidd0123 <wizkidd0123@>

On a side note, the answer is 30 pearls because where
x represents the original number of pearls on the
necklace:

6+(x/6)+(x/5)+(x/3)+(x/10)=x
(6/x)+(1/6)+(1/5)+(1/3)+(1/10)=1
(36/x)+1+(6/5)+2+(3/5)=6
(36/x)+3+(9/5)=6
(180/x)+24=30
(180/x)=6
x=30


		
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