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| (1) Posted by Eugene Rosner [Wednesday, Nov 13, 2013 18:35]; edited by Eugene Rosner [13-11-13] |
when rotating a chess board 45 degrees in Part B....
orthogonals and diagonals swap what do squares a1,b1,a2,b2(in part A) become in part B.?
or is it that the squares remain the same but the function of the pieces change?
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| (2) Posted by Adrian Storisteanu [Wednesday, Nov 13, 2013 19:17] |
I remember Theodor Tauber composed a few problems (some time in the 1970s) with the board rotated by 45 degrees. He might have published an article on this too, I'm not sure ("feenschach" would have been an appropriate place for it?!). His inspiration was a misprinted stipulation, which said 45 instead of 90...
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| (3) Posted by Hauke Reddmann [Thursday, Nov 14, 2013 12:27] |
Mathematically, you can't. So you have to reinterpret.
- You rotate by 45° and round all new positions to the nearest field.
- You rotate and multiply by Sqrt[2] Or divide.
- Whatever. :-)
So, Ke4 Re6 - Kc6 might "rotate" to Kf5 Re6 - Kd5 or suchlike.
Hauke
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| (4) Posted by Sarah Hornecker [Thursday, Nov 14, 2013 16:21] |
I think you'd have a diamond shaped board then where you have the rook line (former fields) a1 to h8, etc.
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| (5) Posted by Eugene Rosner [Thursday, Nov 14, 2013 19:53] |
In Cylcone-I, #625, part B. where is the support of the bishop when 1...g1 2.Bxf1#? Can't the bK grab the bishop?
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| (6) Posted by Torsten Linß [Thursday, Nov 14, 2013 22:46] |
I vaguely remember a short article by N. Shankar Ram (?) in feenschach in the middle or late 1980s on this.
In particular, a knight moving two squares vertically and one horizonally (or vice versa) effectively acts like a Camel...
Maybe somebody can undig that article... (I've binned too many of my chess journals during my first MLC)
Torsten
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| (7) Posted by Eugene Rosner [Friday, Nov 15, 2013 01:16] |
I see how the knight gets converted into the camel by each square now =sqrt2, but how do I visualize the camels movement converting to a knight's move?(I can see it "grow" to a (4,2) leaper but not shrinking to a knight's move...)
what am I missing here?
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| (8) Posted by Jacques Rotenberg [Friday, Nov 15, 2013 09:43] |
To make it easier, you can do this :
Instead of board rotation, you use piece rotation.
You can check it's all the same (out of 000 & 00).
For 45-rotation you can easily see the rook/bishop transformation (and reverse), queen and king don't change, pawns being "berolina".
For Knights you have a choice
- if you see its move as two straight steps followed by one on side, the 45- rotation will give you a camel.
- if you see its move as diagonal one followed by an orthogonal one (or reverse), the 45-rotation will not change it.
So it is more a question of conventions.
However, in both, you can easily see that after 45-rotation + 45-rotation you are back.
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| (9) Posted by Eugene Rosner [Friday, Nov 15, 2013 14:07] |
Jacques-
thanks for the try. I understand all the pieces' transformations EXCEPT the camel. the camel is a 3,1 leaper. rotate the board 45 degrees and its orthogonal movement, 3 up, 1 right produce a 4,2 movement on the unrotated board. how does it shrink to 2,1?
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| (10) Posted by Eugene Rosner [Monday, Nov 18, 2013 23:07] |
Mr. Shankar Ram set me straight. yes the camel's move(3,1) is converted to the long(4,2) upon rotation, but the (2,1) is along the same line and therefore the camel converts to a knight!
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| (11) Posted by shankar ram [Friday, Nov 22, 2013 13:35] |
Glad to be of help, Eugene..
Now.. when do we see your 45 degree problem..? :-)
btw.. coming back here after a long time.. glad to see this forum is still up..
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| (12) Posted by Eugene Rosner [Friday, Nov 22, 2013 18:49]; edited by Eugene Rosner [13-11-22] |
I'm still scheming and ruminating on this! Controlling the flight squares around a bK is most challenging. Your K-battery-rider mechanism makes great sense in your example!
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| (13) Posted by shankar ram [Saturday, Nov 23, 2013 09:47] |
use a couple of paralysing pawns.. :-)
(unless you want the BK to move around..)
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| (14) Posted by Kevin Begley [Saturday, Nov 23, 2013 11:20] |
If the paralysing units are not intrinsic to your thematic idea, show off your composing talent, and avoid them.
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| (15) Posted by Andrew Buchanan [Thursday, Dec 12, 2013 16:30] |
Another way to rotate a square by 45 degrees is shown in the rather old, rather good game, "Sigma File". See this image of the 5x5 board, and follow the lines between the locations:
http://img.auctiva.com/imgdata/7/7/5/0/7/8/webimg/695844785_tp.jpg
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| (16) Posted by Adrian Storisteanu [Monday, Apr 14, 2014 14:41] |
Stumbled upon the article I mentioned: f-65 May 1983, pp.72-73.
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