A 119 Year Quest to Understand Tessellating, Convex, Irregular Pentagons

Michelle TatCommunity Partnerships, Conference Presentations, Library, Museum, Nature & Science Center, Parks & Recreation, We think math is fun!Leave a Comment

The Fifteen Tessellating Pentagons

The idea for MathHappens to work with tessellating pentagons originated from intern Jason Gorst’s suggestions for future projects on his final report. A tessellation describes an arrangement of shapes that tiles a plane with no gaps or overlaps.The challenge of finding all possible tessellating pentagons was issued in 1900 by David Hilbert at the International Congress of Mathematicians in Paris as one of the 23 mathematical problems to solve over the next century. Flash forward one century, and the 15th tessellating pentagon was discovered in 2015, and Michaël Rao proved there are no more tessellating pentagons in 2017. A request from the Thinkery event in Austin featuring women in STEM led MathHappens to search for women in mathematics, and we came across articles about Marjorie Rice. Rice was a self-taught mathematician with no more than a high school education in mathematics. Motivated by her passion for mathematics and an article on tiling, Rice worked on and discovered 4 different tessellating pentagons. Rice took tiling a step further by drawing designs on the pentagon tilings, click through to read her account and scroll down to see her work.

Inspired by Rice’s achievements “for the sake of discovery,” MathHappens featured Marjorie Rice and the pentagons she discovered at the Thinkery Women in STEM event. We started by creating colorful puzzles out of Marjorie’s pentagons numbers 9 and 15 and found that they were interesting for both children and adults. Rice’s creative designs that make tiles interact give people different ways to approach math. After the positive and encouraging reception of the pentagons, we decided to laser cut out all 15 pentagons with the help of intern Ben Duong, and intern Michelle Tat worked on drawing creative designs on the 15 pentagons to make the tiles interactive and fun.

MathHappens has presented tessellating pentagons at the following events:

Nature and Science Center in Summer 2019

Makerfaire Austin and Makerfaire San Francisco 2019

Women in Mathematics at the Thinkery

Austin Museum Day 2019 Presentation

Teacher’s Conference

Gilbert Elementary School

Math Teacher’s Circle


Austin Central Library Kids Block Party

Amy’s Ice Cream


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