From 67298680e5721f58a28f4f662356dee2f5395657 Mon Sep 17 00:00:00 2001
From: fschmnn <31562265+fschmnn@users.noreply.github.com>
Date: Sat, 9 Mar 2019 13:31:37 +0100
Subject: [PATCH] 2019.03.09 - improved readme

---
 README.md | 38 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 37 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f67c85b..4eb499d 100644
--- a/README.md
+++ b/README.md
@@ -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/)