Please pardon the crudity of this new post.  I am learning.

    Be sure to click the solution button to read the text regarding Chess and Geometry link about this position.

I will have further posts, hopefully with alot better illustrations of this excellent checkmate 

 

 

 I know this isn't perfect, but shows what you mean I think. Ignoring the kings of course, which have to be in diagrams (that's annoying, should be able to do diagrams that don't fit chess rules)

 

 

 

 

 

 

 

 

 

 

   Thank you,   that is a good start toward a solution of illustrating in crystal clear graphics the idea of the concentric triangles.

I don't know much about concentric triangles and the like, but for a nicely done video that makes this particular endgame very easy to accomplish, have a look at:

http://www.chessvideos.tv/forum/viewtopic.php?f=12&t=802&sid=756adf1799171b42ad67e3101c491fc1

 

There are a number of other great endgame videos there as well, such as the famous Saavedra Position. As far as B+N goes, after watching the video and practicing just a bit, I now try to steer Blitz games into such positions if I am way ahead just for a bit of fun. I'm still not sure how practical it is to study this particular mating method, but it is fun knowing that you can do it.

The maximum number of Bishops of the same color in accordance with the rules of chess is only 5.  It is impossible to have a position whereby there are more than 5 Bishops either on the black or white square.

No, you can have more. Remember doubled pawns. Theoretically you caould have nine.