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DISCLAIMER: The ideas expressed on this page are the creative work of its author, Charles Gilman, and they might not be shared by others responsible for this website. They do not represent any convention, consensus, or standard regarding piece names.

Man and Beast 03: From Ungulates Outward

Introduction

Representing the nobility of MAB 01: Constitutional Characters and downtrodden of MAB 02: Shield Bearers are radial pieces, which pass through the centre of a cell or only its borders. This article completes coverage of pieces in FIDE Chess by covering oblique pieces, those which pass through the interior of cells missing their centres. The simplest such pieces are coprime leaping ones, defined as simultaneously moving a number of ranks and a number of a files whose only common factor is 1. Most of the more widely-used ones are also symmetric, with no restriction as to which number is the number of ranks, which can be forward of backward, and which the number of files, which can be left or right. Oblique directions vastly outnumber radial ones, and are best defined by their coordinates, the minimum numbers of ranks/files moved. Leap Length is the hypotenuse of the right triangle formed by the coordinates, and different coordinates can have the same Leap Length. As this statistic is often non-integer I use Square Of Leap Length, always an integer, abbreviated to SOLL.

Like steps of a diagonal move, each leap of an oblique move might be further restricted by the One Foot in the Grave rule but generalised for a rectangular, parallelogram, or cuboid block of cells.

The acknowledgments, overview, and glossary to the series can be found here. Established pieces have a link to their Piececlopedia page. The images used in this series, and indeed in most of my pages, can be found here.

Pieces

FIDE Chess has one oblique piece, named after the intermediate rank of KNIGHT and historically the cavalry regiment of ancient India's Chaturanga (fourfold army). Another oblique piece in many historic and modern variants is the CAMEL, as many armies have had camelry regiments. The Knight is a 2:1 leaper, SOLL 5, and the Camel a 3:1 leaper, SOLL 10. The SOLL ratio of 2 is no coincidence. The Camel's relationship to the Knight is exactly that of the radial Ferz and Wazir: as a Ferz move is two Wazir moves at right angles, so a Camel move is two Knight moves at right angles. It can be shown by algebra that coprime leapers on square cells are paired, one (e.g. Knight) with an odd and an even coordinate and an odd SOLL, and one (e.g. Camel) with two odd coordinates and twice the SOLL. If they are respectively the a:b and c:d leapers then c=a+b, d=a-b, a=(c+d)/2, and b=(c-d)/2. Try it with the 1:0 Wazir and 1:1 Ferz, and with the 2:1 Knight and 3:1 Camel. Taking Ca- to mean cavalry (in Napoleonic Chess the Camel is called Light Cavalry), -mel can be a stock ending for two-odds leapers, preceded by (usually) the first consonant and vowel of its one-of-each dual. here are the movement diagrams for the esablished images:

As a piece combining Wazir and Ferz moves, such as the FIDE King, can triangulate - return to a cell in three moves, two orthogonal and one diagonal - so can a Knight+Camel compound, in two Knight moves and a Camel one. This piece is known in both variant and problem circles as a GNU, although Wildebeest is also in currency. These are exact synonyms, as Earl is to Count, meaning another ungulate, a hoofed animal like horses and camels. Gnu has the advantage of Gn- resembling the Kn- of Knight, so -u can be a stock ending for oblique triangulators. This too extrapolates to all pairs of duals. Here is the movement diagram for the obvious image:

The next shortest-range pieces have established ungulate names: the 3:2 ZEBRA, 4:1 GIRAFFE, and (noting that 4:2 is not coprime) 4:3 ANTELOPE. My two-odds duals rule gives a 5:1 ZEMEL, 5:3 GIMEL, and 7:1 NAMEL. Of these only Gimel is a real word, an ancient one from which camel and gamma derive. Its G is hard, unlike Giraffe but in keeping with gamma, the game name Shogi, the fantasy writings of Oxford dons drawn on in themed variants (Tolkien's Gimli and Lewis Carroll's gyre and gimble), and this author's surname! Triangulators can readily take real words: Zebra+Zemel=ZEBU (another ungulate), Giraffe+Gimel=GURU (an Indian holy man, to honour Chess' Indian roots), and Antelope+Namel=ANU (a Mesopotamian sky deity, c.f. the Indo-Iranian Varuna and European Uranus). My Armies of Faith series uses the Anu (page 1) and Guru (pages 2 and 6), and some of my larger Wildeurasian variants use the Zebu and Guru. Here are movement diagrams for the established Zebra and Giraffe images, the pieces' respective duals, and finally the triangulators:

Even-SOLL pieces are colourbound in 2d, meaning that they can reach only alternate squares. This binding extends to cubic 3d boards, but on the hex-prism boards pioneered in Honeycomb Chess they are unbound - able to reach any cell. In the xyrixa geometry, however, as featured in Mark Thompson's Tetrahedral Chess, they are bound to 1 in 2 cells of alternate square planes, making 1 in 4 overall. Odd-SOLL leapers are colourswitching, always moving from one Bishop and Ferz binding to the other, even-SOLL ones rankswitching, always moving from an odd to an even rank or vice versa. This prevents them returning to a cell in an odd number of moves. Odd-SOLL ones retain this property on cubic boards (which retain 2 Bishop bindings) but not on hex-prism ones comprising more hex boards than the longer coordinate. Conversely even-SOLL ones retain it on hex-prism boards (where they always move from an odd to an even hex board or vice versa) but not on cubic ones with at least one dimension exceeding the longer coordinate and all exceeding the shorter. An m:n leaper on a hex-prism board with m or fewer hex boards is bound to 1 in m² cells of 1 in n hex boards. On xyrixa boards m:n leapers can go up m-n levels on one vertical plane and down m-n levels on another bringing them to a cell m+n Wazir steps away in the horizontal plane. For odd-SOLL leapers m+n being odd makes this a move to the horizontal plane's opposite colour, so they are no longer switching. For even-SOLL coprime leapers m+n is even, leaving them switching.

For the 5:2 leaper's SOLL of 29, approximately Saturn's year in Earth years, SATYR (a mythical ungulate as regards at least its rear limbs) gives a 7:3 SAMEL and a triangulating SADHU (another Indian holy man). The 6:1 leaper's established name FLAMINGO, a bird like the radial Rook, suits a direction close to the orthogonal. For other "narrow" colourswitching leapers this inspires a 7:2 STORK, 8:1 BITTERN, and 9:2 ALBATROSS. "He thought he saw an albatross..." is the best known verse of Lewis Carroll's Gardener's Song. Conversely "broad" ones, close to the diagonal of the Bishop, inspire increasingly junior church titles: a 5:4 RECTOR, 6:5 PARSON, 7:6 CURATE, 8:7 DEACON, and 9:8 VERGER. Triangulators include Flamingo+7:5 FAMEL=FLAMBEAU (a torch in a pre-electric sense), Stork+9:5 SOMEL=SOU (an old coin), Bittern+9:7 BIMEL=BIJOU (real-estate euphemism for small), Albatross+11:7 LAMEL=LAMBEAU (obscure heraldic term) Rector+9:1 REMEL=RESEAU (grid or network of lines), Parson+11:1 PAMEL=PARVENU (newcomer to high society), Curate+13:1 CUMEL=KUDU (another ungulate), and Deacon+15:1 DEMEL=DISPARU (French for "one who has disappeared"). Note how all churchmen's duals have short coordinate 1.

Filling in the space between these groups, my final ungulate name is OX (plural OXEN) for the 7:4 leaper. Following interest expressed in covering all pieces with coordinates up to 9 I added 8:3 HUCKSTER, 8:5 AGRONOME (see notes), and 9:4 OUTSETTER - inspired by sharing the SOLLs of the Hamster, Fruitbat, and Upsetter in this article's 3d continuation MAB 05: Punning by Numbers.Further interest from George Duke led me to extend the maximum fully-covered coordinate to 11, in conjunction with similar extension on cubic boards and hex 2d ones. For 10:n leapers I looked to names not clashing either forward or backward with existing piece names, to allow reversal for the 8:6:n leaper with the same SOLL. For "narrow" ones I kept to birds, though based on name rather than size, with a 10:1 MACAW, 10:3 LYREBIRD, and 11:2 QUAIL. Having exhausted churchmen for "broad" ones I turned to the French and Greek concept of the Bishop piece as Fool with a 10:9 ZANY and 11:10 ECCENTRIC. As the 11:8 leaper's SOLL, 185, is the Knight's 5 times the Flamingo's 37 I term this piece FLYBYNIGHT. The rest I fill in with 10:7 RUNAWAY after a similarly flighty person, and 11:4 MYSTIC and 11:6 SCRYER after rôles seen as marginal in today's society.

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The Antelope's leap length of 5 is the Knight's SOLL. This is no coincidence; if c (not necessarily square) is a²+b², then c² is (a²+b²)² = (a²)²+(b²)²+2(ab)² = (a²)²+(b²)²-2(ab)²+4(ab)² = (2ab)²+(a²-b²)². Beyond coordinate 11 I consider only pieces applying this to the Zebra (SOLL=13) and Giraffe (SOLL=17): the 12:5 and 15:8 leapers which I term ZOETROPE and GYROSCOPE. As the Y of Gyroscope, Lyrebird, Mystic, Scryer, and Flybynight is pronounced as a vowel it is treated as one in derived names, where it is pronounced long - and the I of Giraffe and Bittern short to distinguish them.

Triangulators include Ox+11:3 XOMEL=ORMOLU, Huckster+11:5 HUMEL=HUTU (an African tribe), Agronome+13:3 GAMEL=GATEAU, Outsetter+13:5 TOMEL=TORTEAU (two kinds of cake), Macaw+11:9 MAMEL=MARABOU (a bird in its own right), Lyrebird+13:7 LYMEL=LIEU (French for place), and Zoetrope+17:7 ZOMEL=ZULU. I have yet to devise a name for Gyroscope+23:7 GYMEL.

A generalisation of the rule above is that for any a:b and c:d oblique leapers there are two leapers with the product of their SOLLs. This is because (a²+b²)(c²+d²) = (ac)²+(ad)²+(bc)²+(bd)² = (ac)²+(ad)²+(bc)²+(bd)²+abcd-abcd. This can be arranged as either ((ac)²+(bd)²+abcd)+((ad)²+(bc)²-abcd) = (ac+bd)²+(ad-bc)² or ((ac)²+(bd)²-abcd)+((ac-bd)²+(ad-bc)²+abcd) = (a-c)²+(b+d)². Thus the leapers are the ac+bd:ad-bc and bc+ad:ac-bd leapers. The Bittern and Ox are these pieces for Knight/Zebra, and the Albatross and Curate for Knight/Giraffe. The Knight/Antelope ac+bd:ad-bc leaper is the Quail, while the Knight/Satyr, Knight/Flamingo, and Zebra/Giraffe bc+ad:ac-bd leapers are the Verger, Flybynight (hence its name), and Eccentric.

The first-used pure-oblique square-board compound whose components' SOLLs are the same, the BAT giving John Savard's variant Leaping Bat Chess its name, is a compound of the Ox and Bittern. As a flying mammal fits well a compound of a more typically quadrupedal one and a bird, and it influences my naming certain pieces in MAB 05: Punning by Numbers after specific kinds of bat, I gladly acknowledge it. The simple leaps with the next product SOLL, 85, the Knight's 5 times the Giraffe's 17, are the Curate and Albatross. As clergyman+bird=woman has a long precedent for radial pieces I apply the same to oblique ones to name the SOLL-85 compound PRIESTESS. For SOLLS 130 and 170, Bimel+Xomel=COBAT and Lamel+Cumel=COPRIESTESS. As yet I have not gone on to the next product SOLLs, 145/185/221, having named the 9:8/11:8/11:10 but not 12:1/13:2/14:5 leapers. Four sets of four compounds each join up four simple pieces - Bat/Bijou/Cobat/Ormolu for Ox/Bittern/Bimel/Xomel, Priestess/Lambeau/Copriestess/Kudu for Curate/Albatross/Lamel/Cumel. That leaves combinations such as Ox+Bimel. As I had two new endings, I decided to cross over with -ess for SOLL 65+SOLL 130 compounds and -at for SOLL 85+SOLL 170 ones. As the longer SOLL would be the same I needed a tiebreaker for which compound to give the Co- prefix, and settled on prefixing the piece with the longest coordinate, which requiring a larger board would be rarer. Thus Ox+Bimel=BUTTRESS, Curate+Lamel=BUREAUCRAT generates Bittern+Xomel=COBUTTRESS, Albatross+Cumel=COBUREAUCRAT. The Bat and Priestess are colourswitching on rectilinear boards but unrestricted on hex prisms, for the same reasons as the Gazelle. The Cobat and Copriestess are colourbound on rectilinear boards, switch ranks and files in 2d, and switch hex planes on hex-prism boards, for the same reason as the Cogazelle. The Buttress, Cobuttress, Bureaucrat, and Cobureaucrat are unrestricted on all boards for the same reason as the Gnu. Here is the movement diagram for the Bat:

These pieces are unavailable on Pentagonal boards and only those with shorter coordinate 1 - Knight, Camel, Gnu, Giraffe, Zemel, Flamingo, Namel, Bittern, Remel, Macaw, Pamel - on Pentagonal-prism ones. Even those exist only on boards with more levels than the longer coordinate, where they are bound to one in that coordinate levels and move exactly one column at a time. Being averse to 1 in 3 columns of a hex-prism board renders Knights, Giraffes, Zemels, and all leapers with no coordinate divisible by 3, Switching, between the other two groups of columns. It does not affect Camels. You might try working out if it affects Zebras, Antelopes, Gimels, or Flamingoes.

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Shogi has a forward-only (FO) version of the Knight, which following this precedent means directions moving more ranks forward than files sideways. Its Japanese name Keima means "Honourable Horse" but "Honorary Horse" better describes its weakness compared to mainland counterparts! A snappy name to extrapolate from is HELM, a part of Knights' armour sharing the initial of horse. It also has associations with the aforementioned authors. Tolkien has Helm's Deep, and "No one shall speak to the man at the helm" is Rule 42 in Lewis Carroll's preface to the Hunting of the Snark.

Other colourswitching FO leapers of non-integer length are the 3:2 STRIPE; 4:1 BLOTCH; 5:2 VINE, from satyrs' love of wine; 5:4 UMBRELLA and 6:1 MALLET from Lewis Carroll - the first from his magazine The Rectory Umbrella, the second from the use of flamingoes thereas in the first Alice book; 6:5 NOSE, as in poultry; 7:2 GIFT, from the famous white lie "the stork brought you"; 7:4 LABOUR, for which the ox is deployed; 7:6 EGG, the one that was "good in parts"; 8:1 POND; 8:3 TRAY; 8:5 IRRIGATOR; 8:7 ALCOVE and 9:8 CREVICE, from church architecture; 9:2 FLOAT, from the albatross' ability to stay in the air; 9:4 JAUNT, on which one might indeed set out; and 10:1 WARMTH, of the rainforest where macaws live. Note how each name has a different initial. For this reason I made the FO Lyrebird a ZITHER, which like the lyre is a non-bowed stringed instrument, and the FO Runaway a YELL, which is the sound that they might make when fleeing.

For their duals I start with a 3:1 HUMP. The four forwardmost Gnu moves suggest someone with an excess of forelimbs, so I call Helm+Hump HANDYMAN. As these start with H the same names can be used substituting the relevant initial. Thus Stripe+5:1 SUMP=SANDYMAN (a Tolkien character), Blotch+5:3 BUMP=BANDYMAN, Vine+8:3 VUMP=VANDYMAN, et cetera. The -ump rhymes are the basis to Lewis Carroll's Pig Tale, in which "a Camel with a Hump" is a character and bump, jump, and lump rhyme with it. As pieces ending in -man are derived from Handyman, in which -man actually means man, their plurals end in -men. There are obvious images for Helm and Hump, but as there is no miniaturised Wildebeest image I substitute a miniaturisation of the image for a piece rarely restricted to forward directions. Here are the movement diagrams for the Helm first face-to face and then corner, then likewise for the Hump, Handyman, Stripe, and Blotch:

For integer-length FO leapers and their duals I use further names using the same initials, again based on real words starting with H: the 4:3 HASTE (of an antelope fleeing a predator), 7:1 HARDNESS (of enamel), and their compound the HEADMAN (someone favoured by those on high). These extrapolate to 12:5 SASTE+17:7 SARDNESS=SEADMAN and 15:8 BASTE +23:7 BARDNESS=BEADMAN.

The number of most forward directions is more consistent between oblique than between radial directions. On face-to-face square-cell boards and Glinski-level hex-prism boards it is always the 2, on face-to-face cubic ones the 4, and on hex-ranked hex-prism ones the 6, flanking the single forward orthogonal. On Wellisch-level hex-prism boards it is 4 in all - above and below each forward orthogonal - and on corner-column cubic ones those plus the corner square-board pair. FO compounds have this number for each kind of direction. Like radial ones, FO oblique pieces are generally promotable. My variant Partnership Mitregi features an alternative to promotion: each army is moved by a team of two players who have opposite forward directions.

These pieces are unavailable on Pentagonal and Pentagonal-prism boards.

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As well as the Gnu there are established ungulate names for the Zebra's compounds with its components: Knight+Zebra=GAZELLE, and Camel+Zebra=BISON. Neither triangulates in 2d; a Bison can return in 5 moves but a Gazelle is colourswitching because both its components are. The pieces have established imgaes and here are their movement diagrams:

For compounds with both components replaced by their duals, prefixing with Co- gives Knight+Zemel=COBISON and Camel+Zemel the colourbound COGAZELLE. Giraffe compounds not having acquired standard names I add Knight+Giraffe=LOOKOUT (military rôle high off the ground), Camel+Giraffe=MUEZZIN (rôle high off the ground in lands with camels), Zebra+Giraffe=GAMEWARDEN (rôle involving both beasts), and Giraffe+Zemel MIXTURE (of stripiness and blotchiness); the endings -in and -out are a deliberate mnemonic. This trio yield Knight+Gimel=COMUEZZIN, Camel+Gimel=COLOOKOUT, Zebra+Gimel=COMIXTURE, and Zemel+Gimel=COGAMEWARDEN. The Co- piece is always the one with the longest-leaping component. For some Antelope compounds I reuse endings: Zebra+Antelope=DRAWOUT, Giraffe+Antelope=GISELLE, Antelope+Zemel=BRINGIN (opposite of draw out), Antelope+Gimel=PYLON (something tall). This gives Zebra+Namel=COBRINGIN, Giraffe+Namel=COPYLON, Zemel+Namel=CODRAWOUT, Gimel+Namel=COGISELLE. Here is the movement diagram for the Lookout:

Some of my FO compound names are self-explanatory, some refer to armour, some allude to the pattern of the moves. Helm+Stripe=VISOR, Hump+Stripe=TERRACE, Helm+Blotch=GORGET, Hump+Blotch=AERIAL, Stripe+Blotch=COLLAR, Stripe+Haste=JET, Blotch+Haste=ELEVATOR, Blotch+Sump=INFILL, Haste+Sump=DECAL, Haste+Bump=BOLDFACE, Labour+Pyramid=LINEUP (in the sense of batting order), Egg+Float=MAENAD (woman devotee of Bacchus and so a suitably heathen underling to a Priestess), Labour+Pump=FIGUREHEAD (something that sticks out like a buttress), Egg+Fump=WRITEUP. These generate Helm+Sump=COTERRACE, Hump+Sump=COVISOR, Helm+Bump=COAERIAL, Hump+Bump=COGORGET, Stripe+Bump=COINFILL, Sump+Bump=COCOLLAR, Stripe+Hardness=CODECAL, Blotch+Hardness=COBOLDFACE, Sump+Hardness=COJET, Bump+Hardness=COELEVATOR, Lump+Pump=COLINEUP, Eump+Fump=COMAENAD, Pyramid+Lump=COFIGUREHEAD, Float+Eump=COWRITEUP.

For compounds of root-and-square combinations, and of their duals, I make use of the forward-only prefix, again using real words with an initial H- and extrapolating. Knight+Antelope=HOVERCRAFT (fast-moving marine vessel), Camel+Antelope=HAJJ (Islamic pilgrimage), Helm+Haste=HOTSPUR (epithet of the Percy family, alluding to an armoured horseman spurring his horse to go faster), and Hump+Haste=HARDSHIP (as pilgrims may well undergo). These extrapolate to Knight+Namel=COHAJJ, Camel+Namel=COHOVERCRAFT, Helm+Namel=COHARDSHIP, Hump+Namel=COHOTSPUR, Zebra+Zoetrope=SOVERCRAFT, Zemel+Zoetrope=SAJJ, Zebra+Zomel=COSAJJ, Zemel+Zomel=COSOVERCRAFT, Stripe+Saste=SOTSPUR, Sump+Saste=SARDSHIP, Stripe+Sardness=COSARDSHIP, Sump+Sardness=COSOTSPUR, Giraffe+Gyroscope=BOVERCRAFT, Gimel+Gyroscope=BAJJ, Giraffe+Gymel=COBAJJ, Gimel+Gymel=COBOVERCRAFT, Blotch+Baste=BOTSPUR, Bump+Baste=BARDSHIP, Blotch+Bardness=COBARDSHIP, Bump+Bardness=COBOTSPUR.

These pieces are unavailable on Pentagonal boards and only compounds both of whose components have shorter coordinate 1 - Lookout, Muezzin, Cobison, Cogazelle, et cetera - on Pentagonal-prism ones. Even those exist only on boards with more levels than the longer coordinate, and move exactly one column at a time. The Lookout is bound to alternate levels.

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Long-range versions of all the above repeat the move in the same direction subject to not reaching an ally or overtaking an enemy on a "landing place". Most established is that of the Knight, the NIGHTRIDER, and analogous are the CAMELRIDER and ZEBRARIDER. These are distinguishable from the leapers on an 8x8 board, but riders of longer leapers require larger boards. It seems logical to simply add -rider to short-range simple leaper names of five or fewer letters to give e.g. ZEMELRIDER, GIMELRIDER, SATYRRIDER, STORKRIDER, OXRIDER, HELMRIDER, VINERIDER, HUMPRIDER, SUMPRIDER, HASTERIDER. Where the short-range name exceeds five characters I prefer to add -rider to the first five letters. Surely it is clear what is meant by e.g. GIRAFRIDER, ANTELRIDER, FLAMIRIDER, RECTORIDER, BITTERIDER, STRIPRIDER, BLOTCRIDER. Here are the established piece images for the Night-, Camel-, Zebra-, and Giraf- riders:and

Where a compound piece is a pre-existing word, the same rules apply to give GNURIDER, ZEBURIDER, BISONRIDER, VISORRIDER, BATRIDER, GAZELRIDER, LOOKORIDER, PARVERIDER, HANDYRIDER, SANDYRIDER, TERRARIDER, PRIESRIDER, HOVERRIDER. Where it is its dual's name prefixed with Co-, however, curtailment is applied before prefixing to allow up to five letters between prefix and suffix, giving a wider range of names than five letters including Co- would allow. This gives the likes of COBISONRIDER, COVISORRIDER, COGAZELRIDER, COMUEZZRIDER, COTERRARIDER.

These pieces are unavailable on Pentagonal and Pentagonal-prism boards.

In the following illustration of the pattern of piece names every White piece is checking the Black King save the linepieces, which would be were no other piece in their way. Rotated Knights represent pieces with ungulate names, rotated Rooks pieces with bird names, rotated Bishops pieces with clergy and fool names, a speial image the Flybynight, and rotated Pawns pieces with other real-word names.

Notes

Coprime oblique pieces specific to cubic 3d boards have their own article, MAB 05: Punning by Numbers, and those specific to hex boards, 2d and 3d, theirs, MAB 14: Oddly Oblique. MAB 09: Mighty Like a Rose covers Curved and Crooked versions of MAB 03 and 05 pieces, and MAB 16: Diverging Further divergent oblique pieces.

I welcome additions or improvements, but please note how such groups of compound name endings as -elle/-on/-or/-ace, -ut/-in/-et/-al, and -en/-ure/-ar/-ill are preserved, and no two compounds of the same simple piece have the same ending. This is done bearing in mind mixed-range and part-symmetric oblique compounds, which share the page MAB 07: When Beasts Collide with non-coprime oblique pieces and compounds of three or more oblique components. The sets -u/-an and -aft/-ajj/-ur/-ip are reserved for particular geometric combinations. Pieces mixing radial and oblique directions have their own article, MAB 08: Diverse Directions.

Other Far East variants reinforce the convention of Shogi's narrow meaning of "forward". The stepping Knight of Xiang Qi and Janggi makes oblique moves comprising radial steps, and the only moves comprising only forward steps are those taking it further forward than sideways. Likewise Janggi's version of the Elephant, a stepping Zebra. This is also the basis for definitions in other geometries and orientations.

Agronome is an alternative form of agronomist - but both shorter and avoiding the ugly Tsimonorga and its rude-sounding Bishop compound. See also notes on Hylonome in MAB 14.



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By Charles Gilman.
Web page created: 2007-12-02. Web page last updated: 2014-08-10