There is no 'L' in Knight

I should preface this by saying that I am by no means a chess master.  I have a love for gaming, chess in particular, but have never played chess competitively.  Despite this (or, more likely, because of it) my appetite for the game remains unabated, and often I will find myself trying to create a new opponent out of the people sitting near me.  "Oh, a chessboard,"  I might remark, "wouldn't it be a lark to play a quick little game?".  "I haven't played in years, but I think I remember how," they will reply.  And now the trap is set.

We recap the rules and movement of the pieces as we set up the board.  The Pawn's diagonal capture, the Bishop's, Rook's, and Queen's long contiguous paths, the King's slow, omnidirectional plod.  "And the Knight?" I ask.  Invariably, they will tell me that the Knight moves in an 'L' shape.  And this is true.  But I detest it.

Describing the Knight's movement as an 'L' is a twofold problem.  First, it immediately discounts the Knight's unique ability to jump over other pieces.  He is not moving two squares over and then one to either side, he is in factleaping directly to that final square.  Furthermore, to think of the Knight's movement as this sort of  odd little path requires the chess beginner to account for two completely unrelated squares in every move.  For a knight with a full range of movement, this is [8 x 3 =] 24 squares when the knight is only attacking 8.

But the real problem I have with the 'L' description, and the reason for this post, is that it hinders further understanding of the Knight's movement. Consider what happens if we envision the Knight's movement as simply a circle of attack based on his initial position:

 Here we only need to picture the radius of the circle to find the squares under attack (while also possibly considering the restriction that the Knight cannot attack along his current rank and file).  This is substantially less information to hold in mind, and also opens the door to the radial symmetry of the Knight's attack.  We can follow this symmetry deeper, discovering the squares the Knight can attack by move 2:

And move 3:

 And move 4:

If we composite all these moves, it might look something like this:

 Which is, admittedly, a little complicated.  But still manageable.  Now let's look at the alternative:

This is just one of the Knight's paths from move 1 to move 4 (out of a possible 8).  It covers 12 squares.  Here is the full the range of attack using 'L' shapes:

A gordian knot to the beginner, and not much friendlier to those experienced with the game.  We have gone from considering 25 squares (using the method of radial symmetry) to considering [12 x 8 =] 96!

So now I leave it up to you.  The next time you find yourself explaining the rules of chess, try describing the Knight's attack as circular.  It may at first seem a little awkward, a break from tradition, but your student will certainly thank you for it.

(originally posted at blog.spencer-miller.com)