August 1st, 2024

The Japanese Way to Multiply Is So Much Cooler Than Ours (2020)

A viral TikTok video has popularized a graphical multiplication method using sticks, often called "Japanese multiplication," which aids visualization but lacks historical documentation compared to traditional techniques.

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The Japanese Way to Multiply Is So Much Cooler Than Ours (2020)

A viral TikTok video has popularized a unique multiplication method often referred to as "Japanese multiplication," although its origins are unclear and may also be linked to Chinese or Vedic methods. This graphical approach to multiplication uses sticks to represent numbers, allowing individuals with minimal math literacy to visualize and solve multiplication problems. The method mimics traditional long multiplication by arranging numbers in a way that makes it easier to see the calculations. While it works well with smaller digits, it can become complex with larger numbers. The stick method has gained traction online, but there is little historical documentation of its use prior to the last two decades, unlike other multiplication methods such as chisanbop or the Russian multiplication technique, which have well-documented histories. The term "Vedic math" has been co-opted to describe various shortcuts, but its connection to this stick method is uncertain. The method may have been created recently as a visual aid for understanding multiplication, showcasing a design feat rather than a traditional technique. Despite its modern popularity, the stick method serves as an engaging way to grasp multiplication concepts, illustrating the evolution of mathematical teaching methods.

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By @amai - 6 months
This is just the https://en.wikipedia.org/wiki/Grid_method_multiplication .

Actually it is a more complicated version of it. See here for an image showing how to multiply numbers with three digits using that method: https://math.stackexchange.com/questions/886177/where-does-t...

By @jyunwai - 6 months
This looks very cool, though it looks inconvenient for multiple problems due to the amount of drawing involved.

A good, practical approach I've liked to use are the techniques in Benjamin and Shermer's "Secrets of Mental Math." One of the examples in the linked article shows a method of drawing for solving 42 * 21. But this is easier to solve mentally by converting this to a simpler problem, as recommended by the book: 42 * 21 = (42 * 20) + (42 * 1) = 840 + 42 = 882.

You can often split up these types of multiplication problems into an easier multiplication problem, plus an addition. You can then solve the entire problem without much or any paper for calculation.

By @big-green-man - 6 months
Naively this looks like it could be used for any base number system, so from the example, 9*8 looks like it's a raw brute force using this method, but if converted to something smaller, like base 5 as a random example, it could easily be made simpler.

This could also pretty easily be implemented in code as well, although it would almost certainly be less efficient than just letting your language and processor do the math it was already optimized to do.

By @kazinator - 6 months
This is too labor-intensive for anything other than inducing intuition in schoolchildren.
By @an_aparallel - 6 months
The dot division method is related and equally neat