I was wondering how Al Khwarizmi's method of multiplication worked? I was hoping for a simple explanation in layman's terms.

For those of you unfamiliar with the method its basically this:

If you have two numbers, x and y, write them beside each other. Then repeat the following: divide the first number (x) by two , rounding the result (if it has a 0.5 if the number was odd) and then double the second number. Keep repeating till the first number is one. Then strike out all the rows where the first number is even, and add up whatever remains in the second column.

i.e. 11 * 13.

11 13

5 26

2 52 (strike out)

1 104

13 + 26 + 104 = 143

  • 2
    $\begingroup$ I had not seen it ascribed to al-Khwarizmi. The method has many names. It is thoroughly discussed here. You might want to chase down some of the links provided at the end. $\endgroup$ – André Nicolas Mar 10 '12 at 19:17
  • $\begingroup$ Boy,that's a strange algorithm for so simple an operation.But I assume it developed when there was no clear idea of what we call multiplication today. I'm pretty interested in the history of math,but sadly,I haven't studied the work of the medevial Arabian mathematicians that closely.I really should. $\endgroup$ – Mathemagician1234 Mar 10 '12 at 19:22

It's using Horner's method and the distributive property on the expansion of the first factor in base 2.

In your example, $11 = 1011_2 = 2^3+2^1+2^0 = (((1)\cdot2+0)\cdot2+1)\cdot2+1$


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