Here’s Mathematician KP Hart’s Math Question and Answer for Monday, November 23rd!
Twelve Fingers
What if we had twelve fingers and no decimal but a dozen-al system
So ten becomes the new twelve, you need two new number symbols for the old ten and eleven and new words for them, how does that work with the multiplication tables and with arithmetic in general? Then you will eventually need need more new words, for the 100 and the 110, etc. I was lead to this question because things in packaging are easier to distribute in 2×6, 3×4, 4×3 or 6×2.
The system described here is well known. The dozenal, base 12 or duodecimal, system is being used here and there and is for arithmetic a bit more convenient than our decimal system because, as noted in the explanation, 12 has more divisors than 10. You can work duodecimally on one hand: the phalanges of the four fingers (and you count them with your thumb).
Normal arithmetic does not really change: adding and subtracting still works with carrying and borrowing, we would need to learn two more multiplication tables. It would be a good exercise to create some sums and try to do those, say with A and B as the `digits’ for ten and eleven: A+A=…, A×B=…, 12+2B=…, 12×2B=…
And yes, we would need to adopt or invent a few more words to pronounce the numbers. Counting in hide-and-seek would take a bit longer: “eleventy-nine, eleventy-ten, eleventy-eleven, gross … I’m coming”
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Read all of KP Harts math questions here!
About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.
I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim I decided to post answers to those questions, in Dutch. For your edification I will translate these posts into English.
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