It uses polyominoes
which are plane geometric figures formed by joining one or more equal squares edge to edge (refer Figure 1).
Coloring the cells of the grid, stereo learners revisit arithmetic and algebra, meet tessellations, polyominoes
, moires, affine transformations, cellular automata, methods of computer graphics and animation.
Yuan, Lee, and Wang (2010) examined the effects of using virtual manipulatives and physical manipulatives in the study of polyominoes
on junior high school students.
One of the polyominoes
requires a more sophisticated version of the priority strategy called history dependent priority strategy.
Gessel has shown  that the coefficients count convex polyominoes
Pentominoes are a particular group of polyominoes
, a mathematical generalisation of the idea of a domino.
One of the most intriguing of such puzzles involves proving that polyominoes
of a certain shape can be laid down to form a complete rectangle.
We might think laterally and link the word 'tile' with Polyominoes
, or Polyiamonds, as in Solomon Golomb's game of Pentominoes, or variants of Blokus (Figure 3).
He fully described polyominoes
and pentominoes while a graduate student at Harvard where he obtained his Ph.
The last equality follows from the fact that for polyominoes
the difference between the number of salient and reflex angle is exactly 4.
The Geometry Junkyard, Polyominoes
and Other Animals: www.
Several bijective proofs in the literature show that parallelogram polyominoes
are enumerated by Catalan numbers, the two most classical being Delest-Viennot's bijection with Dyck paths [DV84] and Viennot's bijection with bicolored Motzkin paths [DV84].