Saturday, 25 October 2014

Napier's Bones

"Napier's bones" sounds like a religious relic. "Rabdology" (or, the art of casting them bones, if you will) doesn't sound any better.

But Napier's Bones is actually a cool and fascinating calculating device that turns multiplication into addition and division into subtraction. It usually consists of 10 sticks (or columns) each divided into rows which comprise of multiples of the number on the top row, like this:

The 7th bone is highlighted in the image. It starts: 7 x 1 = 7; 7 x 2 = 14; 7 x 3 = 21; etc. The multiples are rendered as single digits divided by a diagonal line.

The use of this calculating device can be a bit tricky in the beginning but figuring it out is 99% of the fun (ie, 'fun' because it actually encourages mathematical thinking and offers up a possibility for some bright mind to explain why it works). In the book, The Joy of Mathematics, by Theoni Pappas, the author herself says that 298 x 7 turns into 165 + 436 but no matter how hard you try and add 165 + 436 to result in 2086 it can only sum up to 601.

It is only by inserting a place-holder zero at the end of the top number: 1650 + 436 does the sum finally equal 2086.

Here is a link that explains in more detail how Napier's Bones work ('s_bones)

I'd also recommend checking this link out: (

Though electronic calculators and computers made devices like Napier's Bones and the slide rule 'obsolete' they are still (and will always be) tremendously valuable as teaching tools. One cannot open up an electronic calculator and see its inner workings. The electronic circuits just don't sweep one up in wonder and delight at the fundamental principles, patterns and properties of numbers that are inherent and immediate in these analog computing devices.

I would encourage Nunavut's elementary and secondary teachers to recruit Napier's Bones and the use of slide rules into their math courses. Who knows, perhaps one or two of their students just might amaze and inspire them; who knows, one of them might actually run the whole gamut themselves and uniquely re-create deeper connections in mathematics, even re-create calculus or engineering principles themselves.


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