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George Duke wrote on 2007-11-07 UTC
Ralph Betza's 500 Comments to mid-2003, when he left, are labelled 'gnohmon'. Betza's nom de plume 'gnohmon' as 'gnomon' means Basic Unit in mathematics. The gnomon is the Piece needed to add to a figurate number to get the next bigger one. A figurate number, including tetrahedral numbers, can be represented by geometric pattern. For example, dots show 'triangular numbers' 1,3,6,10,15 and so on, as the triangle of dots enlarges. Also figurate, square numbers are 1,4,9,16... So the particular gnomon varies with the pattern. In square numbers, 'gnomon' is L-shaped: just wrap a 1x9 bent once 90 degrees into an L-shape, the gnomon, to get 25, 5x5, the next square number. In Tetrahedral Chess, remarkably ''the Pawn rows completely enclose the pieces in the starting position,'' unlike ordinary cubic 3-D, ''so that play begins with pawn development, as in usual chess.''

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