16 July 2012

Changing Bases

I have just started reading Alex's Adventure in Numberland" and in it, he started talking about counting in different bases and how different cultures count (I won't spoil it for you don't worry). One thing he said was learning the times tables would be easier and I can't disagree i.e.

3 times table
  • 3 x 1 = 3
  • 3 x 2 = 6
  • 3 x 3 = 9
  • 3 x 4 = 10
  • 3 x 5 = 13
  • 3 x 6 = 16
  • 3 x 7 = 19
  • 3 x 8 = 20
  • 3 x 9 = 23
4 times table
  • 4 x 1 = 4
  • 4 x 2 = 8
  • 4 x 3 = 10
  • 4 x 4 = 14
  • 4 x 5 = 18
  • 4 x 6 = 20
  • 4 x 7 = 24
  • 4 x 8 = 28
  • 4 x 9 = 30

The reason for it's simplicity is because 12 has more factors 1,2,3,4 and 6, whereas 10 has 1,2 and 5.

I wanted to know whether it was more good looking. When I was in primary school we made shapes on squares paper by using the times tables. First pick a point and then go in a clockwise direction (North, East, South and West) and plot the 2 times table. When you get to a 2 digit number like 14, you add the digits together (1 + 4 = 5) and plot this number.

For example this is base 10. times table 1 to 5.

How does this compare with base 12?

Personally I think base 12 looks better, more patterns. If you are interested there is a UK and USA society dedicated to base 12. These pictures was created using Paint.NET (Windows)(I created the grid myself).