. Grade 8, Illustrative icon
Task

Tile Patterns I: octagons and squares

Illustrative MathematicsVaries

Tiles and tiling patterns are good sources for developing geometric intuition. This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons. There are two steps to the problem, corresponding to the two vital aspects of a square. First, the sides must be congruent: this comes from the fact that the regular octagons enclosing the square are congruent.

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