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Re: Russian Peasant Multiplication: Explained!
Posted:
Mar 3, 1998 9:26 PM
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This article is essentially a duplication. However using your example, I
can now make my previous explanation even simpler.
In article <34FCB257.2C7DF882@ufl.edu>, Kevin Fortin <kfortin@ufl.edu> wrote:
>Thanks to the sci.math readers whose responses helped me to understand
>"Russian Peasant Multiplication"!
>
>Here's my own attempt to explain it:
>
>[Please use a non-proportional font so the columns line up. Also, I
>SNIP<
>Example: 19 x 54 = X
>
>(H = "halving column", D = "doubling column"; in column H, any remainder
>is discarded after each halving.)
>
>_H_ _D_
>54 19 (ignored)
>27 38
>13 76
> 6 152 (ignored)
> 3 304
> 1 608
>
>The even numbers in column H are crossed out, along with the
>corresponding entries in column D across the way. The remaining numbers
>in column D are added up to give the product:
>19 x 54 = (38 + 76 + 304 + 608) = 1026
Now, as I explained in my previous article, all you need to do to explain
this is notice that when the left-hand column is even, the product of the
two columns remains the same when you move down to the next line.
(For instance, 54 * 19 = 27 * 38.) However when the left-hand column is
odd, this is not quite correct. The discrepancy is in fact the number in
the right-hand column. (For instance, 27 * 38 = 13 * 76 + 38.)
Now if you take the final entry in the right-hand column and add to it
all the discrepancies, i.e. all the other entries in the right-hand
column which appear next to odd numbers in the left hand column, you
recover the original (unknown) product. (As you indicate, 54 * 19 =
608 + 304 + 76 + 38. The point is that 54 * 19 = 27 * 38 =
13 * 76 + 38 = 6 * 152 + 76 + 38 = 3 * 304 + 76 + 38 =
= 1 * 608 + 304 + 76 + 38. )
In my opinion, bringing binary numbers into the explanation just makes it
more confusing.
See <Http://www.math.Hawaii.Edu/~lee/elementary/Lazy2.pdf> ("Bride of
the Lazy Man").
--
Trying to understand learning by studying schooling
is rather like trying to understand sexuality by studying bordellos.
-- Mary Catherine Bateson, Peripheral Visions
lady@Hawaii.Edu
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