Using Symmetry to Learn Coordinates

By leveraging the symmetry of the chessboard, you can cut the information you need to memorize in half. Learn techniques using horizontal, vertical, and point symmetry.

A chessboard has 64 squares, but you don't need to memorize each one individually.
By focusing on the symmetry of the chessboard, you can reduce the amount of information you need to remember.

The Three Symmetries of the Chessboard

1. Horizontal Symmetry (File Symmetry)

The board is symmetrical along the center axis between the d-file and e-file.

LeftRight
ah
bg
cf
de

Applications:

  • If you know where a3 is, h3 is "the same rank on the opposite side"
  • If you know b7, g7 is its horizontally symmetric position
  • If a knight is on b1, the opposite knight is on g1

This symmetry helps understand the relationship between the kingside and queenside.

2. Vertical Symmetry (Rank Symmetry)

The board is symmetrical along the center axis between the 4th and 5th ranks.

White's SideBlack's Side
18
27
36
45

Applications:

  • White's castling destination g1 and Black's g8 are vertically symmetric
  • White's pawn starting rank (2nd) and Black's (7th) are symmetric
  • Once you learn White's piece placement, Black's follows automatically

3. Point Symmetry (Central Point Symmetry)

There is point symmetry around the center of the board (the intersection of d4, d5, e4, e5).

SquarePoint-Symmetric Square
a1h8
a8h1
b2g7
c3f6
d4e5

Point-symmetric squares are on exactly opposite sides of the board's center.

Efficient Learning Using Symmetry

The "Only 32 Squares" Strategy

Using symmetry, you only need to memorize half the board.

Method 1: Split by Rank

  1. Memorize the 32 squares on White's half (ranks 1-4)
  2. Derive Black's half (ranks 5-8) by vertical reflection

Method 2: Split by File

  1. Memorize the 32 squares on the queenside (files a-d)
  2. Derive the kingside (files e-h) by horizontal reflection

Either method cuts your memorization in half.

The Relationship Between Square Colors and Symmetry

There's an interesting relationship between symmetry and square colors:

  • Horizontally symmetric squares: Different colors (e.g., a1 is dark, h1 is light)
  • Vertically symmetric squares: Same color (e.g., both a1 and a8 are dark)
  • Point-symmetric squares: Same color (e.g., both a1 and h8 are dark)

Knowing this rule lets you deduce a square's color from its symmetric counterpart.

Practical Applications

Practice with Coordinate Quizzes

  1. First, try coordinate quizzes with only ranks 1-4
  2. Once comfortable, add ranks 5-8 while consciously using symmetry
  3. Practice instantly deriving symmetric relationships like "e3's vertical symmetric is e6"

Learn in Pairs

Being aware of point-symmetric pairs lets you remember two squares as one piece of knowledge:

  • a1-h8 (both ends of the diagonal)
  • b2-g7 (common knight destinations)
  • c3-f6 (important bishop and knight squares)

Application in Games

Understanding symmetry is useful in actual games:

  • Opening knowledge learned as White can be applied when playing Black
  • Kingside attack patterns can be applied to the queenside
  • It becomes easier to see the board from your opponent's perspective

Conclusion

By leveraging the chessboard's symmetry, you don't need to memorize all 64 squares individually.
Understanding the three types of symmetry—horizontal, vertical, and point—cuts the information you need to remember in half.

Combined with the anchor point method, you can navigate the board even more efficiently.
Start by being conscious of vertical symmetry (the correspondence between White and Black).