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Turning chess. Pieces can turn 45 degrees after movement. (8x8, Cells: 64)
George Duke wrote on 2008-07-19 UTCGood ★★★★
In Turning Chess, Betza's first example is Pawn 1 f2-f3 (turns right), 2 f3-g4 (right) 3 g4-h4 (no turn). That Pawn can never move again. Notice the optional ''turning'' after a move is always 1/8, same as saying 45 degrees. Betza postulates Turning Bishop and Rook having same value. In 2004 Comment Gilman takes exception that there is no such thing as Turning Knight, alleged by Betza within the article, and rather Knight turned logically becomes Camel. It leads Gilman in subsequent years to explore in depth all the angles involved for purposes of nomenclature, classification, and further invention of fairy-Chess-piece moving modalities.

David Paulowich wrote on 2007-06-06 UTCGood ★★★★

I believe Ralph Betza is saying that a Mao becomes a Moa, and vice-versa, after what he calls a 45 degree turn. Thus the Knight is unchanged by turning. With regard to Charles Gilman's comment, I must admit that I find the Camel uninteresting, both as a chess player and a mathematician.

Charles Gilman wrote on 2004-10-14 UTC
```'There is no such thing as a Turning Queen because all rotations are
identical; it turns but stays the same. This is also true of King and
Knight, and it means that they do not benefit from the value boost that
true Turning pieces get.'
It is not true of Knights as Knight moves are not at exact 45° intervals.
Just as a 45° turn on the radials (i.e. Rook <=> Bishop) involves
mutiplying or dividing distances by root 2, so it does with oblique
dirctions. Thus a Knight making a 45° turn would be come a Camel (and vice
versa).```