This week I’ll be running a workshop, “The Problem with Pentagons”, for Math for America teachers.
The workshop focuses on the classification of pentagonal tilings of the plane. Although humans have been tiling with polygons for hundreds of years, the answer to the question “Which pentagons can tile the plane?” was only recently answered!
The surprising story of pentagonal tilings spans cultures, centuries, and disciplines. In addition to some beautiful geometry, the story is also filled with lots of twists and turns that illustrate the many ways in which mathematics happens. It’s a wonderful opportunity to bring living, breathing mathematics to our students, and I’m looking forward to discussing the many classroom connections with MfA teachers.
I can’t recall ever seeing this tiling before. It reminds me of the Old Woman / Young Woman optical illusion: Sometimes I see overlapping octagons and sometimes I see disjoint hexagons and squares. The photo also seems impossible to straighten: No matter how I rotate it, it always appears crooked in some way.
I was surprised to see this structure overhead. It brought to mind the theorem about parallel lines creating congruent arcs when intersecting circles, as well as one of my favorite math photos.
