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Knight. See Knight. Makes a (1,2)-jump.
Charles Gilman wrote on 2003-04-27 UTCGood ★★★★
As this page shows the Knight's move on both square and hexagonal boards, it is worth noting how differently it plays on the two boards. As an elemental leaper it cannot 'lose the move' on a square (or square-based 3d) board - that is, it can only get to cells of a different colour in an odd number of moves, or the same colour in an even number of moves. On a hexagonal board it can return to its starting square in 3 moves as well as in 2, or an orthogonally adjacent on in 2 as well as in 3!

Charles Gilman wrote on 2003-06-08 UTC
By convention the piece in the hexagonal diagram is given the same name as that in the square one, but it is really very different, quite aside from py previuos comment that all hex pieces can lose the move. The square-board Knight is a root 5 leaper. Its move and multiples thereof are linked to the Camel (leap length root 10) by a rotation of 45º and ratio of root 2. The hex Knight is a root 7 leaper, which does not exist on square boards or even cubic 3d ones! Its move is linked to a root 21 leaper by a rotation of 30º and ratio of root 3.

Anonymous wrote on 2004-06-22 UTCExcellent ★★★★★

Kuyan Judith wrote on 2008-04-13 UTC
I have noticed some pages in this site (I forget which ones) described the 'hippagonals' as 'the lines halfway between diagonals and orthogonals'. They are not. The hippagonals are at inverse tangents of -2, -.5, .5 and 2 from forwards, which are at about 26.6 degrees from the orthogonals (18.4 degrees from the diagonals). The lines halfway between the diagonals and orthogonals are 22.5 degrees from each, and will not cross the centres of any squares no matter how big a board they are on.

Souen wrote on 2008-09-03 UTC
In this page, you translate the French 'cavalier' as 'knight', but in fact, it means 'rider' or 'horseman' (the French for 'knight' would be 'chevalier'). The chess piece is indeed 'cavalier' in French.

George Duke wrote on 2008-09-21 UTCExcellent ★★★★★
Jumper as piece-type. The greatest utility is thinking of sliders as special case of larger category multi-path (to be continued). Old-fashioned terms, when variants were more arcane field, are leaper, slider, rider, hopper, as in George Jeliss' ''All the King's Men.'' Old also twenty years now from 1990 are ''multi-path,'' and two-way; three-way or three-path came in 1992; four- and more 1996 for four-stepping Scorpion. In the oldest Glossary (Jeliss) is ''Darter'' for blockability along radial lines of Bishop and Rook. Darter would have to be piece-type unto itself but for newer convenience of ''Multi-path'' designation(t.b.c.) Then a decade ago, after all the foregoing, appears in CVPage glossary term lame equivalent to darter. Betza chose to use ''lame'' in two articles after 2000 for Dabbabah and possibly Alfil. Newest term of all is bifurcation piece for Winther's inventions, constituting new piece-type. Leapers of real utility only number five, Dabbabah, Alfil, Knight, Camel, Zebra. Of those Knight occurs over 95% of instances of leaper and all others 5%. Are there still other Leapers? Hardly any reduced to practice with much frequency. Lavieri's Altair's Grand Bishop compounds with what Jeliss calls (3,3) Tripper. Betza's Half-Duck is compound of what Gilman calls(0,3) Trebouchet + D. + Ferz. Does that exhaust Leapers in actual CVs outside the standard box of five (N,D,A,Camel,Z)? That's over 99% of the usages, NDACZ -- like perhaps 99% of openings exclude Rooks' Pawns. I know several dozen others (the 1%) no one would be interested in besides Gilman and myself. So, Leapers implemented are the smallest category of piece-type. On 8x8 theoretically would there be only the 63 simple leapers? Presumably that is the moot point, because only the five get, or likely to be, used. Leaper, headed by this Knight, predating Chess, is one conveninet category of piece-type, fully exhausted by five all of the above, as a practical matter.

George Duke wrote on 2008-09-24 UTC
I mean to change the estimates to about Knight 85%, Dabbabah 4%, Alfil 4%, Camel 4%, Zebra 1%, all others 2%. There is difficulty when many CVs are within large systems like in fact just-commented Michael Howe's Novo and Optima, my own Baseball(at CBM3) and 91.5 Trillion, and Betza's 30-40 large systems in individual articles, such as Different Augmented Knights. I believe ADK alone Betza claims has tens of thousands CVs; and others' ridiculously as many as 10^50. Practical standard leapers number five in 98% of cases, the NDACZ.

Rodrigo Zanotelli wrote on 2014-04-06 UTC
kuyan its possible to think about knight as a piece that moves to "the closest square to him, not on rook lines and bishop lines"

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