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World Tessellation Day

Try creating your own tessellation using paper, pen, and scissors to help wrap your mind around these strange and fascinating math-based patterns.

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Activate creative communities and educators with a niche STEM-art observance that drives engagement around DIY craft supplies, educational content, and themed events.

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Share tessellation DIY tutorials and challenge followers to create their own patterns using household items
Host a virtual or in-person tessellation contest with prizes for best designs, encouraging user-generated content
Partner with art/craft retailers to promote supplies (colored pencils, specialty paper, scissors) with tessellation project bundles
Create educational content linking tessellations to nature, architecture, and famous artists like M.C. Escher

History

World Tessellation Day, celebrated on June 17th, has an interesting history. It was started in 2016 by Emily Grosvenor, an author known for her children’s book “Tessalation!”

This day was chosen to honor the birthday of M.C. Escher, a Dutch artist renowned for his use of geometric patterns to create mesmerizing artworks. Escher’s work significantly contributed to the popularity of tessellations, patterns that repeat without overlapping or leaving gaps, in both art and mathematics.

The purpose of World Tessellation Day goes beyond celebrating Escher’s legacy. It aims to engage people of all ages in exploring the fascinating world of tessellations. These patterns are not just mathematical concepts but are found in nature, art, architecture, and technology.

The day encourages exploration, creativity, and appreciation for the intricate patterns that make up the world around us. From the Sumerian civilization’s early examples of tessellations to their use in Roman and Islamic art, tessellations have a rich history that reflects their broad applications.

Emily Grosvenor initiated World Tessellation Day with the help of math educators and enthusiasts to celebrate the beauty and uses of tessellations. It’s a day for people to share their love for patterns and to discover the creative and mathematical aspects of tessellations.

Whether through creating artwork, exploring nature, or participating in educational activities, World Tessellation Day offers an opportunity for everyone to appreciate the connection between math and art.

How to celebrate

Craft Your Tessellation Art

Grab some colored pencils, scissors, and paper; it’s time to get crafty! Anyone can transform simple shapes into repeating masterpieces. Just remember, the goal is to fill a space so completely that not even a tiny ant could crawl through a gap. It’s a puzzle, an art project, and a brain teaser all in one!

Nature’s Tessellations Treasure Hunt

Head outside for a tessellation scavenger hunt. Nature is the original artist, crafting patterns in turtle shells, honeycombs, and pineapples. Challenge yourself and your friends to find the coolest, most intricate patterns. The winner gets bragging rights and perhaps a nature-inspired prize.

Tessellation Party Time

Why not throw a themed bash that would make Escher proud? Invite pals over for tessellation-inspired snacks (think checkerboard cookies, hexagon honeycombs) and activities. You can even have a contest for the best-tessellated outfit. May the best pattern win!

Educational Escapades

Dive deep into the world of tessellations with documentaries or online courses. There’s a wealth of knowledge out there that can turn anyone from a novice to a tessellation titan. Share your newfound wisdom with friends or on social media. Spread the tessellation love far and wide!

FAQ

What are the basic rules a shape must follow to form a true tessellation in mathematics?

Mathematically, a tessellation of the plane is a way of covering a flat surface completely with shapes (called tiles) so that there are no gaps and no overlaps anywhere. In a standard geometric tessellation, each tile is a closed shape, the interiors of different tiles do not intersect, and any point on the plane lies in at least one tile. For regular tessellations, the tiles are congruent regular polygons arranged so that the same number meet in the same way at every corner.

Why are there only three regular tessellations of the plane?

In ordinary Euclidean geometry, only equilateral triangles, squares, and regular hexagons can form regular tessellations of a flat plane. The reason is that the interior angles of the polygons must add up to exactly 360 degrees at each vertex with an integer number of polygons meeting at that point. Only these three regular polygons have interior angles that divide 360 in this way, which is why mathematicians have proved there are exactly three regular tessellations.

How do tessellations appear in nature, and are they mathematically perfect?

Patterns that resemble tessellations occur frequently in nature, but they are usually approximate rather than perfectly regular. Honeycomb cells, for example, form an almost regular hexagonal tiling that efficiently divides space and minimizes wall material, a property studied in the “honeycomb conjecture.” Cracked mud, dried lake beds, and some biological tissues show networks of polygonal “cells” that tile a surface, though the shapes and angles vary. These natural patterns often arise from physical processes like energy minimization and mechanical stress, so they echo mathematical tilings without matching them exactly.

What role do tessellations play in Islamic geometric art?

Islamic geometric art makes extensive use of tessellations composed of repeated stars, polygons, and interlaced strapwork to decorate walls, floors, and domes. Craftspeople historically constructed these designs using ruler-and-compass constructions that generate patterns capable of covering a surface without gaps. Many famous monuments, including the Alhambra in Spain and mosques across the Islamic world, feature complex tilings that art historians and mathematicians analyze as sophisticated tessellations with rich symmetry and sometimes quasi-periodic structure.

How did Islamic tilework influence M. C. Escher’s tessellation art?

M. C. Escher visited the Alhambra and other sites with Islamic geometric ornament in the 1920s and 1930s and carefully copied many of the tilings he saw there. These studies helped him understand how shapes could interlock and repeat across a surface, which he then adapted into his own system of “periodic drawings” using recognizable figures like birds, fish, and lizards. Articles on Escher’s work note that the structure and logic of Islamic tessellations provided a key stepping stone between historical decorative art and his modern mathematically inspired prints.

How are tessellations used in modern computer graphics and 3D modeling?

In computer graphics and 3D modeling, tessellations are used to break complex shapes and surfaces into simpler pieces that software can store, render, and manipulate efficiently. Curved surfaces are typically approximated by meshes of triangles or quadrilaterals that tessellate the surface, while “tessellation shaders” in modern graphics pipelines can dynamically subdivide polygons to add detail. These tilings make it possible to display smooth-looking objects on screens that ultimately draw only flat polygons.

Why are hexagonal patterns, such as honeycomb and graphene, so important in science and engineering?

Hexagonal tessellations are important because they combine efficient packing with favorable physical properties. The nearly regular hexagons in a honeycomb minimize the total length of walls needed to enclose equal areas, which conserves wax and energy for bees. In materials science, graphene consists of carbon atoms arranged in a two-dimensional hexagonal lattice that tiles the plane, a structure that gives it unusual strength, electrical conductivity, and flexibility. Similar hexagonal and “re-entrant honeycomb” tilings are also used in engineered lightweight panels and mechanical metamaterials to control strength and deformation.