Dozenal

I’ve fallen in love with ‘Duodecimal’.  That is, using base twelve rather than base ten. Dozenal if you will.

# Why? #####

Ten (herein utilising the character “£” wherever it is relevant.) is divisible by two & five. Twelve is divisible by 2, 3, 4 & 6.  It is the first of the superior highly composite numbers (SHCNs), making it a very versatile number.  Its multiplication table is actually simpler than ten’s!

Because dozen is divisible by so many factors the pattern of the respective table is quick to repeat itself. 

Let us look at 3x table. 

First base ten, following the predictable chant:

Three times one is three …

The least significant digit traipses through all the digits till it gets to thirty. That is, 3,6,9,12,15,18,21,24,27,30 and finally 33. 

In contrast dozenal it would look like: 3; 6; 9; 10; 13; 16; 19; 20; 23; 26; 29; 30; and finally 33;. Anything that is a multiple of three will end in either 3, 6, 9, and 0! 

What about 4 times tables? 4,8,12,16,20,24. Pretty simple, no? In dozenal it is 4,8,10,14! Let’s put them on top of each other. 

Base ten:     4,8,12,16,20,24.

Base doz:    4,8,10,14

And so it goes for all numbers that are multiples of dozenal factors.

 
As you can see the majority of the numbers have a smaller, regular pattern. Not forgetting we have two extra numbers, here is the times tables for ten (£)  & eleven (€)

 

However there are two numbers missing. 5 & 7.  7 in both decimal & dozenal is odd, possibly a result of being a prime non-factor of the base.