The Egyptians used heiroglyphics for numbers, and they used a system similar to the Roman numeral system to represent numbers. The stroke ( I ) meant one, the heel bone (U) meant ten, the scroll ( @ ) meant one hundred and they had symbols for the other powers of ten up to one million (the glyph for an astonished man). Using combinations of these symbols, they could express any number they chose. For example, eleven would be UI. Ninety-three would be UUUUUUUUUIII. As you can see, this requires a lot of symbols for relatively small numbers. And, additionally, you can't develop the kinds of algorithms we have for multiplication using this kind of a system.
But the Egyptians had an ingenious way of doing multiplication, very similar to the way computers do it today. It was a method of doubling, because doubling numbers is very very easy. After all, to double UI, you just need another copy of UI. And then it's obvious that UIUI is UUII or twenty two.
How it works.
We'll multiply 9 by 12. We know the answer should be 108. Let's see how it works:
Start two columns, one headed with the number one the other headed with the number twelve. (I won't use Egyptian symbols, since they are cumbersome). Double the values in both columns repeatedly, until the first column contains only numbers that are less than the first multiplicand (the 9).
1 12
2 24
4 48
8 96
We stop here, because the next doubling will give us 16 in the first column, which is more than 9.
Now, locate all of the values in the first column that you can use to create 9 (you'll notice this is a unique combination of values; there aren't multiple ways to create 9 using 1, 2, 4, and 8.) We notice that 1 and 8 are 9, so we go to the second column and pick out the matching values, 12 and 96, and add those up. The result is 108, just as it should be.
Why it works.
Repeated doublings cause "multiplication" by powers of 2 to happen. So, the value in the 1's row is 12x1. The value in the 2's row is 12x2. The value in the 4's row is 12 x 4 and so on. The distributive property allows us to see that if we add 12 x 1 + 12 x 8, it is the same as doing 12 x (1 + 8) or 12 x 9.
This method works for any two numbers you care to try.
5 comments:
You lost me here. If U is 10, how can U be 11? And how can 9 U, which should be 90, be 93?
I was thinking the same thing...Either something is missing when you typed it, or I am not quite such a smart person. Love ya!
Jess
Apologies, apparently, the character I used to represent one was eliminated. I'll fix it.
Well, of course, this makes sense now! Thanks for the update.
Completely understand now! My genius status has been restored!!!!
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