Egyptian multiplication (idea)

Egyptian Multiplication: One possible result of a night of Egyptian sex.

But on a more mathematical note, the style of multiplication used in ancient Egypt is a rather interesting process. What we know of this system came from the translation of the Rhind Papyrus. The actual procedure they used for multiplying utilized no single operation more difficult than doubling. Also, as a big fan of powers of 2, seeing this method really blew my mind.

First, a general algorithm to multiply A*B

Step 1: Create a vertical column starting at 1 (2⁰); list all powers of 2 down the paper (unless you happen to have a sheet of authentic papyrus lying around) stopping at the largest value that does not exceed B.

Step 2: Make a second vertical column to the right of the first, starting with the value A. In each row below A write the double of the row above it. Continue in the manner until this column has as many rows as the column in step 1.

Step 3: (A little knowledge of binary makes this step a breeze) mark off the rows such that the figures in the left column that are marked total to exactly B.

Step 4: Sum up the marked numbers from the right column and you're done! Easy as pi.

Now, a specific example of this algorithm, using actual numbers. Let us multiply together 18 and 43

Step 1: the powers of 2

	1
	2
	4
	8
	16
	32

Step 2:  the matching doubles of A

	1	18
	2	36
	4	72
	8	144
	16	288
	32	576

Step 3: flag the desired rows (1+2+8+32 == 43)

	1	18  -
	2	36  -
	4	72
	8	144 -
	16	288
	32	576 -

Step 4: add up the flagged figures from the second column:

18+36+144+576 = 774

See also:
Egyptian Division
Egyptian mathematics