A very interesting pictorial method to perform multiplication of two numbers has instantly caught my attention. Any two numbers (arbitrary number of digits in each) in decimal form (well, you can extend this to any finite field as well) numbers could be multiplied. Well, this is not my invention. It came as an Email forward (a video showing the method. Unfortunately, I cant upload the video onto this blog). I have prepared some examples, I myself worked out using this method.

Example: Multiply 21 x 35
1.Draw two lines corresponding (two lines for digit2. For 7 draw 7 lines) line for the first digit of 21
2.Draw a line parallel (at a distance) corresponding to the second digit (here 1, in the example 21. Hence draw a single line)

3.Draw the next line at a perpendicular position (only for clarity; The angle doesn’t really matter). Draw 3 lines for the first digit (3) and 5 lines (at a distance) for the second digit (here 5 as in 35).
4. Partition the regions based on the interconnect. Count the number of joints and write down the number of joints from top left to bottom right. If the number of joints are more than single digit, carry forward the left most digit to the previous number. See the figure for illustration

While this method appears to be a lot simpler, I don’t think this is computationally more efficient. The counting complexity need to be considered while you implement this in logic. However, this is quite a nice method to perform multiplication pictorially. The theory is not that complicated. Essentially the normal multiplication steps are represented in a more pleasing structure (matrix like).