Dozenal/fschmnn-duodecimal
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@ -1,6 +1,7 @@
# duodecimal
Python converter/calculator for the duodecimal numeral system (1,2,3,4,5,6,7,8,9,X,E)
## How to use
```python
from duodecimal import duo
```
@ -18,6 +19,41 @@ f = duo(20) / 'X'
```
The decimal representation can be accessed via
```python
g = duo('X.31)
g = duo('X.31')
g.dec()
```
## Why base12?
We use base10 because of the number of fingers we have and not because it is easy to use. While it might be handy for counting, it has serious disadvantages for arithmic operations. This is because 12 has more divisors and hence most sequences in the multiplication table are shorter
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | E | 10|
|--|---|---|---|---|---|---|---|---|---|---|---|---|
|1 |1 |2 |3 |4 |5 |6 |7 |8 |9 |X |E |10|
|2 |2 |4 |6 |8 |X |10 |12 |14 |16 |18 |1X |20|
|3 |3 |6 |9 |10 |13 |16 |19 |20 |23 |26 |29 |30|
|4 |4 |8 |10 |14 |18 |20 |24 |28 |30 |34 |38 |40|
|5 |5 |X |13 |18 |21 |26 |2E |34 |39 |42 |47 |50|
|6 |6 |10 |16 |20 |26 |30 |36 |40 |46 |50 |56 |60|
|7 |7 |12 |19 |24 |2E |36 |41 |48 |53 |5X |65 |70|
|8 |8 |14 |20 |28 |34 |40 |48 |54 |60 |68 |74 |80|
|9 |9 |16 |23 |30 |39 |46 |53 |60 |69 |76 |83 |90|
|X |X |18 |26 |34 |42 |50 |5X |68 |76 |84 |92 |X0|
|E |E |1X |29 |38 |47 |56 |65 |74 |83 |92 |X1 |E0|
|10|10 |20 |30 |40 |50 |60 |70 |80 |90 |X0 |E0 |100|
another advantage is that more fractions have nice representations.
| | base10 | base 12|
|-----|:------:|:------:|
| 1/2 | 0.5 | 0.6 |
| 1/3 | 0.3333 | 0.4 |
| 1/4 | 0.25 | 0.3 |
| 1/5 | 0.2 | 0.2497 |
| 1/6 | 0.1666| 0.2 |
| 1/7 | 0.1429 | 0.186E |
| 1/8 | 0.125 | 0.16 |
| 1/9 | 0.1111 | 0.14 |
| 1/10| 0.1 | 0.1250 |
| 1/11| 0.0999 | 0.1111 |
| 1/12| 0.0833 | 0.1 |
For more information visit [Dozenal Society of America](http://www.dozenal.org/)