Hiding in Plain Sight: Vyshyvanka Secret Codes

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In the following activities, participants hide or reveal words and shapes within beautiful symmetric designs. What can you do with these ideas? Build quick puzzles for friends. Craft folk art pieces to display or wear. Make cute gifts and holiday cards celebrating someone’s name, favorite letter, or motto.

Math word snowflake

Vyshyvanka is an embroidered Ukrainian shirt. Each region in Ukraine has its own traditions for vyshyvanka colors and designs. You can see some of them in this map of Ukraine, “embroidered” region by region:

Embroidered Map of Ukraine

Art: Embroidery artists from Luhansk Photo: Qypchak on Wikipedia

Vyshyvanka designs connect to mirror and rotational symmetry (geometry), isometric transformations (algebraic geometry), and wallpaper and frieze groups (group theory). The activities are accessible for very young children and engaging for mathematicians young at heart.

In 2022, Natural Math organized several math circles and festival activities about vyshyvanka art. These activities are for students, teachers, and parents. Here are some materials from these events for your family or group.

Bluebird Math Circle, Alliance of Indigenous Math Circles, July 2022

Bluebird MC Vyshyvanka newsletter  Bluebird MC Vyshyvanka recap

Download the newsletter and the recap of the activities.

Paper Snowflakes and Mirror Books

To start exploring hidden symmetries, we play with paper snowflakes and mirror books. These maker activities help us to “touch the symmetry” and explore it by hand. Mirror books are our favorite math toys of all times. They are so accessible that even toddlers can play, yet complex enough to engage adults. Likewise, paper snowflakes are traditional in many countries, because it’s a great activity for the whole family.

To fold nicer and to notice more math, play with edges and corners as you go. Before folding, picture each fold in your mind. Which edge must fold on top of which edge? Trace the two edges with your hands before folding them together, to get a good feel. Which corner must fold on top of which corner or edge? Poke the corners to feel them, too.

Snowflakes Math Circle Spark - Natural Math Mirror Books Math Circle Spark - Natural Math

Download two-page printable files from Natural Math circles with Chapel Hill Math Circle: Snowflakes and Mirror Books.

Moebius Noodles Cover

These activities first appeared in the “Moebius Noodles” book, published by Natural Math. Download: “Moebius Noodles” chapters with games centered on symmetry.

Free software

Online vyshyvanka designer https://www.ornament.name/creator: hide words and phrases in symmetric designs.

Math Vyshyvanka

Rotational symmetry doodle pad http://weavesilk.com/ is a meditative, easy to use tool for a quick warm-up or a wrap-up activity. The controls help students learn the language of rotational symmetry.


Wallpaper groups doodle pad https://eschersket.ch/ will invite even a young child to play and explore. The controls introduce formal terminology.

Escher Sketch

Web searches and links

Different people get inspired by different images and stories. Large collections enable stronger personal connections. That’s why it helps to teach everyone in your group where and how to browse for a given math topic.