Napier's Rods

John Napier invented his abacus rods in the early 17th century. Among other things, Napier's Rods can be used for multiplying two factors, and is an ingenious way to multiply multi-digit numbers. 

You'll need about a dozen craft sticks, a ruler, a pencil, and some other markers if you want to gussy up your sticks.

Start by measuring and marking half-inch increments on the craft sticks. I keep extra space at the top. First, make a guide rod, which makes the first column, and is composed of digits one through nine. 

For all the digits zero through nine, make diagonal lines on the sticks from the top right to the bottom left. 

You will then construct a times table for each digit. Multiply the stick's number -- the number at the top -- by the number on the guide stick to the left.

You can make as many sticks as you want, especially if you want to multiply pi to 12 places. If you do have duplicate digits in a factor, make sure you have enough rods. You can always use the back of a stick.

Napier's rods were a refinement of the Arab lattice method imported to Europe by Fibonacci. Add the place values in each parallelogram, carrying when necessary, and you have a quick way of multiplying multi-digit by single digit numbers.

Example: 9 x 314 = 2 1000s + 8 100s + 2 tens + 6 ones. 

How is the lattice method different from standard multiplication? Is it just a different way to project the carried digit? Can you make binary base rods? Joshf made four-sided Napier's Bones. Can you make these with chicken bones? You could print the rods and paste them on to foam core. Here's a set of rods my wife made on a laser cutter -- for my birthday!