Yet such achievement is possible to White and with exact play it seemingly is a certainty that he succeeds in one or the other, owing to his inestimable privilege of first move.
For the normal advantage that attaches to the first move in a game of Chess is vastly enhanced by a peculiarity in the mathematical make-up of the surface of the Chess-board, whereby, he who makes the first move may secure to himself the advantage in mobility, and conversely may inflict upon the second player a corresponding disadvantage in mobility.
This peculiar property emanates from this fact:
The sixty-four points, i.e., the sixty-four centres of the squares into which the surface of the Chess-board is divided, constitute, when taken collectively, the quadrant of a circle, whose radius is eight points in length.
Hence, in Chessic mathematics, the sides of the Chessboard do not form a square, but the segment of a circumference.
To prove the truth of this, one has but to count the points contained in the verticals and horizontals and in the hypothenuse of each corresponding angle, and in every instance it will be found that the number of points contained in the base, perpendicular, and hypothenuse, is the same.
For example:
Let the eight points of the King’s Rook’s file form the perpendicular of a right angle triangle, of which the kindred first horizontal forms the base; then, the hypothenuse of the given angle, will be that diagonal which extends from QR1 to KR8. Now, merely by the processes of simple arithmetic, it may be shown that there are,
- 1. Eight points in the base.
- 2. Eight points in the perpendicular.
- 3. Eight points in the hypothenuse.
Consequently the three sides of this given right angled triangle are equal to each other, which is a geometric impossibility.