Napier's bones


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John Napier was a mathematician who lived in the 16th century. His main achievement was the invention of logarithms, but he also invented a calculating device which was in use until the 20th century. The device was made of rods but the most expensive examples of these rods were made of horn or ivory - hence they became known as Napier's bones.

The 'bones' consist of a set of rectangular rods, each marked with a counting number at the top, and the multiples of that number down their lengths. Multiples are written across the diagonal of a square.  

To multiply one number by another you need to align the digits as they are positioned in the given number against the row of multiples as shown. You look for a number that you are multiplying your large number by and read the results from right to left by adding the digits in each square diagonally in the appropriate row. Multiplication is thus reduced to addition.

For example: to multiply 249 by 9, you need first to position your rods to get the first rod followed by rods beginning with 2, 4, and 9 aligned (or put into a frame).  

Add the numbers diagonally in the 9 th row and look from right to left:


and then diagonally

6+8=14 - write 4 and remember 1 to take to the next row

8+3=11, add 1 from the previous and remember 1 to take to the next row

1 and add one from the previous row

hence the result is 2241.

You can do incredibly long calculations using Napier bones.



Find more about John Napier and logarithms.

You can download the pdf file to make Napier's bones by clicking on the number man below. Then stick the page onto a card and cut the bones out and pronto - you will have your own Napier's bones!

You can neatly put them into a box like the one on the left: there's a little project for you!

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