Thursday 27 May 2021

Smaller Circular Boards

Here are four tours on the smallest circular boards, with at least 12 fixed corners on the circle. These show boards with radii 5, root-50, root-65, root-85 corresponding to the smallest double-pattern fixed-distance leapers. The first three tours show 90 degree rotational symmetry but the fourth only has 180 degree rotation, due to the quarter-board containing an even number of cells (64). 

Radius 5

Radius root-50

Radius root-65

Radius root-85

There are 17 other two-pattern fixed-distance leapers to consider before the first three-pattern leaper of this type (root 325) is encountered, as used in the large tour previously shown. I doubt if I will get round to constructing examples of all of these! 

There is a certain arbitrariness concerning which cells, whose corners go beyond the circle, should be included or not.






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