2-d numbers




1. description



2. examples



3. higher order numbers



4. applications


4a. co-ordinates on maps, engineering diagrams


4b. locations in space

	locations of cities, ships, aircraft etc.


4c. colours


4d. orientations

	orientation of an object in 3-d space

	3 points to orientate neutral position

	2 rotations
	

	note is a separate reading from the position (of the centre) in space


4e. GCS  global co-ordinate system






appendices


a. formal definition

b. conversion macros






text
----



A 2-d number is a new type of number that can represent a point in space. Normally it takes two
numbers to locate a point on a flat surface, and three values to locate a point in space.

2-d numbers have a large number of practical applications as well as being a theoretically sound idea.




description
-----------


take a square area and divide it into four squares




	+-----------+-----------+
 	|	    |	        |
 	|	    |	        |
 	|      0    |	  1     |
 	|	    |	        |
 	|	    |	        |
	+-----------+-----------+
 	|	    |	        |
 	|	    |	        |
 	|      2    |	  3     |
 	|	    |	        |
 	|	    |	        |
	+-----------+-----------+




number the regions 0, 1, 2 3 or alternatively 1, 2, 3, 4


chose a point at random somewhere in one of the four squares


the digit for that square forms the first digit of that number



	+-----------+-----+-----+
 	|	    |	  |     |
 	|	    |	0 |  1  |
 	|      0    +-----+-----|
 	|	    |	  |     |
 	|	    |	2 |  3  |
	+-----------+-----+-----+
 	|	    |	        |
 	|	    |	        |
 	|      2    |	  3     |
 	|	    |	        |
 	|	    |	        |
	+-----------+-----------+



divide that square into four and locate which of the squares the point is in

this numer forms the second digit of the number



	+-----------+-----+-----+
 	|	    |	  |     |
 	|	    |	0 |  1  |
 	|      0    +-----+-----|
 	|	    |	  | .   |
 	|	    |	2 |  3  |
	+-----------+-----+-----+
 	|	    |	        |
 	|	    |	        |
 	|      2    |	  3     |
 	|	    |	        |
 	|	    |	        |
	+-----------+-----------+


The point near the 3 has a 2-d number location of approximately 1303.


Repeat the process of dividing into smaller squares down to as fine a detail as is needed for the practical 

application.



1) the example is a base-2 number, the square can be divided into 9 regions (base 3), 16 regions (base 4) etc.


2) the example covers a flat surface, in space the same applies but cubes are used instead of flat squares.


3) There is no need for the square to be a square, the reference area can be a rectangle (or rectangular cube).


4) the location can be converted to cartesian, or polar coordinates. This requires 'n' values on n-dimensional space.