Can you build "magnified" pattern block triangles, rhombi
, and trapezoids as described below?
The flow f is called shattered iff there is no pair of overlapping f-flat rhombi.
Rhombi which are not f -flat, but g-flat, are called critical rhombi.
In the case where there exists a critical rhombus that is not overlapping with any other g-flat rhombi, we can find well-directed cycles [c.sub.1], [c.sub.2] on [RES.sup.b](f) that split c in the sense that [gamma]([c.sub.1 + [c.sub.2]) = [gamma](c) and l([c.sub.1]) [less than or equal to] l([c.sub.2]) < l(c).
Another student, Lily, decided to organize her counting as follows: "I put the blocks on and took them off as I counted by ones, twos, threes, and sixes." Varley further described the counting methods that some of her students used: "Gaddis used all blue rhombi
and simply counted by twos.
* First, they placed three rhombi on top of a hexagon so that the surface area of the rhombi matched the surface area of the hexagon.
* Finally, they counted the total number of rhombi used: twelve.