John Napier: His Life, His Logs, and His Bones - Napier's Bones

Author(s):
Michael J. Caulfield (Gannon University)

Finally, a hands-on experience will almost certainly surprise the students while also sharing another aspect of Napier’s life. He would take objects that were relatively straight, such as sticks or bones, and inscribe the multiples of one or the other of the single digits (up to the product of the digit and nine). For example, he might have the following for “6”:

These objects came to be known as Napier’s bones (or Napier’s rods). You can use old Popsicle sticks to create your own or buy new ones from a craft store. You will need many sticks for each digit, not only so that several students can do this at the same time, but also because you need one stick for each occurrence of a digit in a factor. When digits are repeated, so are "bones."

The bones were used to expedite the multiplication process as can be illustrated in the following example. Suppose we want to multiply 4972 by 673. As long as your students bear in mind that 673 = 600 + 70 + 3, and that the distributive property applies to 4972(673) = 4972(600 + 70 + 3), they should be able to follow Napier’s procedure.

Despite the fact that the essential features of this procedure are the same as the ones our students learned when they learned multiplication in elementary school, they are generally surprised and delighted to find the “bones” working as they do. Once you have done the hard work of creating lots of these bones, either physically or through an animation like the one below, you will be able to delight your students as well.

Click on the link above to see how it is done. Be sure to stress to your students that, although we are surely multiplying here in an unusual context, we are doing nothing but the ordinary multiplication algorithm. A multiplication problem thus becomes an addition problem through the use of Napier’s bones.

Michael J. Caulfield (Gannon University), "John Napier: His Life, His Logs, and His Bones - Napier's Bones," Convergence (July 2010)