Date: Jul 4, 1994 12:24 PM
Author: Heidi Burgiel
Subject: Marvelous Old Way of Multiplying

A friend of mine just told me a clever historical technique for
multiplying that he read about. It allows one to multiply just by
doubling and halving groups of pebbles.

I'll describe the process using numbers.

Write down the first and second numbers (integers) in your
multiplication problem.

Successively halve the second number, rounding down each time.

Next to the list of halves, put the doubles of the first number.

For 9*14 you'll get a table that looks like:

9 14
18 7
36 3
72 1

Now cross out all the rows that have an even number in the right
column. The sum of the numbers in the left column is the product.

18 + 36 + 72 = 9*2 + 9*4 + 9*8 = 9*14

I believe the computation was originally performed by doubling and
halving the contents of separate bowls of pebbles, "crossing out" by
discarding certain bowls of stones, and totaling by pouring all the
stones into one bowl.

Happy Independence Day!


Heidi