At the beginning of the month I posted about a neat Japanese visual method for multiplying smallish numbers. Besides its sheer visual attractiveness, it’s interesting in allowing one to multiply numbers without reference to multiplication tables (which, let’s face it, typically require rote memorization).
As I mentioned last time, my interest in multiplication is linked to my interest in generating Mandelbrot plots, which is a multiplication-intensive process. But for those learning math, digging into basic multiplication has some instructive value.
With that in mind, here are some other multiplication tricks.
123 × 321 = 39,483
My interest in number multiplication goes back to exploring algorithms for generating Mandelbrot plots, which can require billions of multiplication operations on arbitrary precision numbers (numbers with lots and lots of digits).
Multiplying two numbers — calculating their product — is computationally intense because of the intermediate Cartesian product. Multiplying two 12-digit numbers creates a 24-digit result (12+12), but it also has an intermediate stage involving 144 (12×12) single digit multiplications.
Recently I learned an intriguing Japanese visual multiplication method.
Today’s earlier post got into only the beginnings of abacus operation — mainly how to add numbers. To demonstrate how they have more utility than just adding and subtracting, this Sideband tackles a multiplication problem.
This also illustrates a property of abacus operation that doesn’t arise with addition. With pen and paper, we multiply right-to-left to make carrying easier. Because of the way an abacus works, multiplication has to work left-to-right.
The process is simple enough, but has lots of steps!