Japanese multiplication | Tangente
Japanese multiplication
How can you multiply without a calculator—or even knowing your multiplication tables?

How can you multiply without a calculator—or even knowing your multiplication tables?

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Can a polygon be cut from a sheet of paper with a single straight cut? Surprisingly, the answer is yes! More surprisingly still, this also applies to other objects.

With the advent of calculators and, later, smartphones, people have become less and less likely to work out a multiplication, division or square root by hand. Yet for centuries this was a problem, inspiring a host of ingenious ways to streamline calculations. One such invention was Napier's bones, which effectively automated multiplication.

It is hard to believe that the multiplication and division methods we learn at school did not become universally adopted in the West until the 18th century. So how did people calculate before then? They used calculation aids such as counting boards.

Before the advent of modern technology, techniques or tools had to be devised to perform the basic calculations required by craftspeople, engineers and everyone else! From John Napier to Édouard Lucas, mathematicians distinguished themselves in this pursuit.
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