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The art and math of tiling

The main mathematical news

1985: Stein discovers the 14th type of pentagonal tiling of the plane.

2015: Mann, McLoud, & Von Derauthe discover the 15th pentagonal tiling.

2017: Rao proves there are no additional ways to tile the plane with convex pentagons.

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Additional Theorems / conjectures / Open questions

*   In how many ways can we tile the plane by polygons, vertex-to-vertex and edge-to-edge, without gaps and overlaps?

*   Kepler: There are 11 ways to tile the plane with regular polygons – three by using one polygon, and eight by using several polygons.

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The main mathematical concepts / Principles

*   Regular polygons

*   Symmetry

*   Tiling

*   Plane

*   Angle, Vertex, Edge

*   Convex polygon

*   Reflection

*   Translation

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