# Chinese (?) multiplication

/OK. So my wife posted this video to my facebook page with the question "true or false?"

It's cute and it has the advantage of appearing to make the "complicated" act of multiplication more visual by reducing it to drawing some lines and counting their intersection points. But did you notice that the examples all had small digits? As in, \( 123\times 321 \). This one trick makes the whole thing appear simpler.

But let's try this one: \(78 \times 89\). Here's the picture of the calculation I did using this method:

First note that I made a mistake, getting the wrong answer on the first try. That was because I confused which number of lines was crossing another in each of the four blocks. Only after I checked my answer with the "western" method did I realize I had done something wrong. To see just how inefficient this method is, consider the block on the right side of the diamond. It has \(8\times 9 = 72\) intersection points. Let's assume I can count that many things in a small area correctly. Then I have to do it three more times. Then I have to add up the numbers in the top and bottom columns and get that correct. Then I have to carry the \( 7\) from the right block and add it to the \(127\) in the middle and then carry the resulting \(13\) to the left to get the final answer \(6,942\). Whew.

And, this is really the same as the algorithm you learned in elementary school. It's just in disguise. I suppose this is a useful instructional tool to help motivate the general algorithm, but as a practical computational tool I'd say it falls short. We now return you to your everyday lives in which you're probably using a calculator to do this anyway, if you are multiplying numbers at all.