Comments/Ratings for a Single Item

Oblique.(4,5) is Rector; he leaps 4 then 5, or 5 then 4, same difference if with oppositely orthogonal start to the path, since it is a leap, like Knight (1,2) or (2,1), which could mean the very same square. 4 and 5 share no multiplicative factor, so mathematically they are coprime, prime to each other. Why leave out pairs like (2,4), which are not coprime because they have common factor of 2? Because (2,4) is a Nightrider square, and we would rather get there another way than a direct leap. So would (2,6) be Camel-rider second step not coprime. Gilman is omitting non-coprime, because they would be redundant. (8,10) would be Rector-rider and needs no other name. Surrounding 13x13 set of squares to its central departure square is illustrative. We figure the zero(0) squares of Rook either way within one quadrant (the Rook is the border) as coprime for convenience. So, within 13x13 we are only omitting, with the order mattering, (2,2) (3,3) (4,4) (5,5) (6,6) (2,4) (2,6) (3,6) (4,6) (4,2) (6,2) (6,3) out of 48 squares one quadrant, and that's 25% of them. As we go farther out, about the same ratio obtains. All together oblique directions increasingly outnumber the mere two radial ones, but the omissions to naming would stay nearly the same percentagewise, because of the rider-phenomenon, also able to be called non-coprime redundancy. So Gilman is going ahead with naming most of the squares in principle (he is not likely to proceed beyond 15- or 17-block) or approving already-existing names. [See Pritchard's 'ECV' under Pieces for ancient schema for 7x7 block of squares around a central starting square]

'We figure the zero(0) squares of Rook either way within one quadrant (the Rook is the border) as coprime for convenience.' Far from it, as MAB 06 confirms. Just as 1 being the only self-coprime number renders the Elephant, Tripper, Commuter &c non-coprime pieces, 1 being the only number coprime with 0 renders the Dabbaba, Trebuchet, Cobbler &c non-coprime pieces. 'So, within 13x13 we are only omitting, with the order mattering,' and regarding 0:0 as already occupied: 0:2, 0:3, 0:4, 0:5, 0:6, 2:0, 2:2, 2:4, 2:6, 3:0, 3:3, 3:6, 4:0, 4:2, 4:4, 4:6, 5:0, 5:5, 6:0, 6:2, 6:3, 6:4, 6:6. The comment '(he is not likely to proceed beyond 15- or 17-block)' at least is true, as I only went as far as I did in response to interest in such pieces in this article's previous incarnation.

Actually Gilman has gone to at least surrounding set of squares 27x27 for some incomplete naming. Giraffe is (1,4) leaper pre-Gilman. Two Giraffe moves at right angles reach (3,5) Gimel, and those pieces are called duals with SOLL 17 and 34. It always works that way 1:2 in same sort of pairing as Knight-Camel and Wazir-Ferz. It's interesting. The omitted ''-rider'' squares are important too because they have basal unit starting with Knight etc. And to be addressed later I think multi-path Scorpion 3, Dragon 4 squares (not pathways), Phoenix 6, and Roc 7 are more aesthetic organization of squares. For example, using block of squares 23x23, a larger board than any formally in CVPage, PARVENU is (PARSON + (11,1)PAMEL). Those are duals, Parson and Pamel, as Parson is regular (6,5) leaper and its dual is (1,11) because SOLL of Parson is (36+25) or 61, and the one with SOLL twice that, 122, is (1,11). Expect PARVENU to be able to triangulate, as with any compound of duals. You can sort of play around with duals in that you have more information than you need. Either SOLL alone or the piece-type coordinates can get you to one's dual for each oblique co-prime. It becomes over-determined who the various counterparts are, oblique piece, dual, and compound. // (1) The first prime is 2 not 1. (2) Gilman has mentioned '06' and '08' and we will get to those.