Tag Archives: Cartesian product

Go Forth and Multiply

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.

Continue reading