Russian Peasant method vs Ancient Egyptian method

The Russian Peasant method and the Ancient Egyptian method are related because they both employ the same fundamental mathematical concept of decomposing numbers into binary form and then using halving, doubling, and summation to perform multiplication. They are different interpretations of the same basic technique.

Edited

For example: Multiply 17 by 12 using the Russian peasant method

17 in binary is 10001 and 12 in binary is 1100.

Left             Right

10001           1100

01000           11000

00100           110000

00010           1100000

00001           11000000

Now, cross out the rows where the number in the left column is even.

Left             Right

10001           1100

00001           11000000

Finally, add up the numbers in the right column: 1100 + 11000000 = 11001100

If we convert this binary result back to decimal, we get 204. Therefore, 17 * 12 = 204

The connection to binary representation is evident in the halving process in the left column. By repeatedly halving the number, we are essentially breaking it down into its binary components. The doubling process in the right column corresponds to multiplying by powers of 2.

Comments

  1. stephalafNovember 3, 2023 at 6:07 PM

    Hi Shawn, nice noticing of the half/doubling. I wonder if you might expand on your mention of binary. In what way?

    ReplyDelete
  2. Shawn FanDecember 6, 2023 at 3:27 PM

    Hi Susan, l added one example to show the half/doubling in binary representation.

    ReplyDelete
  3. Susan GerofskyJanuary 8, 2024 at 1:36 PM

    Thanks for this interesting revision, Shawn!

    ReplyDelete

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