A Knight's move is as in chess, an L shaped move, 2 squares in one direction and 1 square in the other direction.)

A Knight's Tour is one where the knight passes through each square exactly once.

You may start on any square you wish.

* For extra credit, come up with a re-entrant tour: at the end, the knight is exactly one knight's move away from the starting square.

* For EXTRA extra credit, make sure that the path is, in some way, symmetrical.
_______________________

Since "Knight's Tour" is a term used outside the scope of this problem, I'm sure you can find an answer on the internet. Please find an independent solution.

This does not require a computer program.

Symmetrical Knight Tours can be done on various boards sizes such as 6x6 and 10x10.  I've found it very difficult to make a symmetrical Knight's Tour on an 8x8 board.  The first 59 moves of the following 8x8 re-entrant tour develop symmetry around the chessboard.  However, the last five moves break the symmetry, but do allow for a closed tour. 

b6-a8-c7-e8-g7-h5-f4-h3-g2-e2-c3-b1-a3-b5-d4-c2-a1-b3-a5-b7-d8-e6-f8-h7-g5-f3-h2-f1-d2-e4-g3-h1-f2-d1-b2-a4-c5-a6-b8-d7-f6-g8-h6-g4-e5-f7-h8-g6-h4-g2-e1-d3-c1-a2-b4-c6-a7-c8-e7-d5-e3-f5-d6-c4-b6

If you connect move 59 (d5) to (b6), you have 60 squares with symmetry.

To see additional Knight Tours and how to make them, check out http://www.borderschess.org/KnightTour.htm.