Hippogonal

A hippogonal (pronounced /hɪˈpɒɡənəl/)^{[citation needed]} chess move is a leap m squares in one of the orthogonal directions, and n squares in the other, for any integer values of m and n.^[1] A specific type of hippogonal move can be written (m,n), usually with the smaller number first. A piece making such moves is referred to as a (m,n) hippogonal mover or (m,n) leaper. For example, the knight moves two squares in one orthogonal direction and one in the other, it is a (1,2) hippogonal mover or (1,2) leaper.

For a (m,n) leaper the occupation of others than the destination square plays no role, thus a (2,2) leaper (Alfil) moves to the second square diagonally and may thereby leap over a piece on the first square of the diagonal. A (m,n) leaper can, by the usual convention, move in all directions symmetric to each other, thus e. g. a (1,1) leaper (Ferz) can move in the four directions (1,1), (1,-1), (-1,1) and (-1,-1).

Other hippogonally moving pieces include the camel,^[2] a fairy chess piece, which moves three squares in one direction and one in the other, and thus is a (1,3) hippogonal mover. The Xiangqi horse is a hippogonal stepper and the nightrider is a hippogonal rider.^[3]

The pieces are colourbound if the sum of m and n is even, and change colour with every move otherwise.

Etymology

The word hippogonal is derived from the ancient Greek ἵππος, híppos, 'horse' (knights used to be called horses, and still are in some languages),^[3] and γωνία (gōnía), meaning "angle".^[4]