Play Truchet: Using the Truchet Tiling to Engage the Public with Mathematics

Year: 2018 Authors: Cindy Lawrence

Core claim

Truchet tilings can effectively combine mathematics and art to create public-facing activities that reveal hidden messages and spark broad engagement.

Topics

Truchet tiling, math outreach, hidden messages, public engagement

Domains

tilings, combinatorics, symmetry, generative design, public art, interactive installation, graphic patterning

Methods

tile arrangement, group construction, tabletop game, large-scale demonstration

Media

square tiles, quarter-circle cubes, wall tiling, challenge cards

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Bridges 2018 Conference Proceedings

Play Truchet: Using the Truchet Tiling to Engage the Public with Mathematics

Cindy Lawrence

National Museum of Mathematics, New York, NY, USA; lawrence@momath.org

Abstract

David Riemann presented a paper at Bridges 2009 that demonstrated use of the Truchet tiling to embed hidden messages in what appears to be an abstract design. The National Museum of Mathematics (MoMath) has used this technique multiple times, in everything from restroom décor to large-scale public demonstrations. This talk will share the exciting math outreach that was inspired by Dave’s creative paper.

Experiences with Truchet Tiling at the National Museum of Mathematics

Square tiles split along the diagonal into two triangles of contrasting color (“Truchet tiles”) were first described in the early 1700s by Sebastian Truchet. A variation on this tiling, using two quarter-circles connecting the midpoints of adjacent sides, was popularized in 1987 by Cyril Stanley Smith. At Bridges 2009, in his paper titled “Text from Truchet Tiles,” [1] David Riemann presented an application of this later version of the Truchet tiling in which structured sections are interspersed among a generally random field. Riemann demonstrated how a simple Truchet contour could be used to represent letters and numbers, creating a visually pleasing tiling that on first glance appears random, but on closer look provides a secret or hidden message.

At George Hart’s suggestion, the National Museum of Mathematics (MoMath) took advantage of Riemann’s clever combination of mathematics and art to create the unique tilings in the Museum’s restrooms. To many visitors, the colorful wall tilings are simply an abstract design, but to those who take a moment to look more carefully, mission-focused messages appear. These tilings have become a favorite feature of the “Hidden Math” tours at MoMath.

Figure 1: Hidden messages in the Museum’s restroom tiling: “Figure it Out!”

Lawrence

Several years after its opening, and after seeing the positive public engagement with the restroom tilings, MoMath innovated to create two messages on the same field, one in each of the two colors, each visible at a different angle. This tiling became the basis of a 200-person group construction at the Museum’s annual fundraiser, followed by an amusing disclosure of the two hidden messages.

(a)

(b)

(c) Figure 2: Group construction (a) of “Partisan Patterns” at MoMath’s annual gala (b); “Vote for MoMath” appears on both the right and left wings of the completed construction (c).

Play Truchet: Using the Truchet Tiling to Engage the Public with Mathematics

Going a step further, MoMath decided to turn this tiling into a tabletop game, providing challenge cards and sets of tiles that people could use to “race” – who could replicate the indicated design as quickly as possible?

Figure 3: “Tetra Truchet.”

The engagement and delight with this game led to a bigger thought: what if we turned this tiling into a larger-scale game, using giant cubes colored with the Truchet pattern? The result was delightful: kids and adults alike loved racing to build the indicated design, as well as building their own abstract patterns comprised of an “aesthetically pleasing, meandering set of mostly closed curves.” An interesting mathematical question arose: “How many possible ways are there to design these cubes so that the black and white pattern continues unbroken over all twelve edges?” Other mathematical questions are also interesting to consider: “How many different ways are there to orient the original Truchet tile (in two dimensions) vs. Smith’s revised tile?” These and other questions will form the basis of new activities and educator sessions at MoMath this fall.

Figure 4: “Play Truchet.”

Lawrence

Figure 5: “Play Truchet” at Math Metropolis: the New York Math Festival (2017).

David Riemann’s innovative use of a mathematical tiling and the Bridges conference are thus responsible for the engagement of thousands of members of the general public, with the “Play Truchet” cubes making appearances at the National Math Festival, at two different World Science Festival installations, at Math Metropolis: the NY Math Festival, as part of the NYC Flatiron Business Improvement District’s Winter Solstice celebration, and with the many youth who attend MoMath’s teen and tween social programs.

(a)

(b) Figure 6: NYC Flatiron Business Improvement District’s Winter Solstice Celebration. “Happy Solstice 2016” (a) is the finished message created by event attendees (b).

Acknowledgements

With gratitude for David A. Reimann’s inspiring 2009 paper and George Hart’s innovative ideas.

References

[1] D. Reimann. “Text from Truchet Tiles.” Bridges Conference Proceedings, Alberta, Canada, Jul. 26-30, 2009, pp. 325-326. http://archive.bridgesmathart.org/2009/bridges2009-325.pdf. [2] C. Smith. “The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy.” Leonardo, vol. 20, no. 4, 1987, pp. 373-385. https://muse.jhu.edu/article/600574/pdf