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Go  Coordinate  System

Coordinate system used for presentation of Go positions and sequences on this web site differs from the generally accepted coordinate system with numbers and letters.  There's no doubt that any coordinate system with clearly distinguishable symbolics will be adequate for position description.  From this point of view it was quite natural to adopt two most widely used sets of symbols: numbers and letters.

However, this presentation that has only one reference point origin of its coordinate system (left bottom corner), and thus doesn't make any use of the natural symmetry of Go board.  Common sense suggests that there's something artificial in counting coordinate displacements from the left bottom corner only, while other corners are equally good for that.  It's worth mentioning that customary practice of designating certain points on the Go board follows the pattern of "counting from the corner" any corner.  When we say "33 point" it's clear to anyone that this is the point of the intersection of 3-rd vertical and 3-rd horizontal lines that can be in any of four Go board corners.  I.e., specific corner itself is often irrelevant, what's important is the location relative to the corner, and for most practical purposes it makes sense to use the closest corner when describing any specific position.

It is easy to see that Go board has horizontal, vertical, diagonal (both), and central symmetry.  This fact prompts the idea to convert the common practice of "counting from the corner" into a coordinate system not with one, but with four reference points all four corners of the Go board.  Such coordinate system that combines the "closest corner referencing" approach with the the necessary coordinate uniqueness for each point of the Go board was suggested by Dmitry Andreev in the middle of 1970-th in Leningrad, USSR (back then; St. Petersburg, Russia as of now at the turn of millennium).

This system introduces the notion of coordinate direction (nothing special about that), and has four coordinate origins four Go board corners (this is unusual, but proves to be quite handy).  Coordinate of each point on the Go board consists of two signed digits horizontal and vertical displacements from the corresponding cornerCombination of coordinate signs determines the corner from which this specific coordinate is a displacement of.

It was quite natural to use direction signs identical to mathematical coordinate notation, i.e., "+" for Up and Right and "" for Down and Left.  Center lines (for 19x19 Go board) have displacement 9 from any corner, and get prefixed by "=" for consistency of notation.




  +0  =9  -0
-0 +---+---+ -0
   ¦ 2 ¦ 3 ¦
=9 +---+---+ =9
   ¦ 1 ¦ 4 ¦
+0 +---+---+ +0
  +0  =9  -0
              

 +---- Horizontal coordinate
 ¦
+i+j   1-st quadrant (++)
+i-j   2-nd quadrant (+-)
-i-j   3-rd quadrant (--)
-i+j   4-th quadrant (-+)
   ¦
   +-- Vertical coordinate
              
+0 +1 +8 =9 -8 -1 -0
-0   -0
-1   -1
-8   -8
=9   =9
+8   +8
+1   +1
+0   +0
+0 +1 +8 =9 -8 -1 -0

This coordinate system is very convenient for keeping game record, and for placing positions and sequences on the board it's easy to find right points even if coordinates are not inscribed on the board.  Simple manipulation with signs can place position into any corner of the board. 

Span of coordinates is different for the boards of different size as can be seen on the diagrams below, but the underlying principle of using all four corners as coordinate origins is the same.



19x19  Go  Board  (Full  Size 361  Points)
 
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13x13  Go  Board  (about Half  Size 169  Points)
 



9x9  Go  Board  (about Quarter  Size 81  Points)
 


Three Go boards shown above have the same measurement size and different grid pitches only for the convenience of their presentation on computer screen.  The real Go boards have different measurement sizes and the same grid pitch one that matches the size of a Go stone.

All recorded Go sequences on this web site use the described system of coordinates, and it's interpretation is programmed in all Go content generation JavaScripts.


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