Eulerian Triangles Shawl Crochet Pattern

Hundreds of tiny triangle motifs come together to create a lacy play of positive and negative space in the Eulerian Triangles Shawl. And surprisingly, there are only six ends to weave in at the end of the project!

You don’t have to understand the mathematical concept that makes this possible. That work has been done for you. All you have to do is obey the instructions and follow the path that is set out for you.

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Eulerian Paths

In case you are wondering:

“In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph which visits every edge exactly once. Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. ” -Wikipedia

While this may not be a true Eulerian path/circuit/whatever, the idea is that you can start crocheting in one place, make partial triangles on a predetermined path, then come back and finish the triangles. All of this is accomplished without ever breaking the yarn.

It’s easier to understand when the pattern is in front of you, and the yarn and hook are in your hand!

The Yarn

The pattern calls for fingering weight yarn in three colors. You’ll need about 435 yds [398 m] each of colors A and B and approximately 230 yds [210 m] of color C.

For the sample, I used Stunning String Twinkle, which has a nice little bit of metallic sparkle. It took one skein each Spring Iris (A, pictured here), Plum Frost (B), and Regal Purple (C). Stunning String even has kits available for $75, which include both the pattern and the yarn pictured.

While you can use any fingering weight yarn, keep in mind that the shawl will need to be blocked fairly aggressively to show off the openwork. The fiber content of the yarn will play a role in your blocking.

Also, because of the path the yarn takes, a color-change yarn may be not be the best choice. One pattern tester found that her initial short color-change yarn obliterated the pattern. Another found that her long color-change yarn worked fine up to a point, but toward the end it created a problem. Therefore, I suggest you use a solid color yarn for each of the three colors. (I’m making a second shawl in Stunning String Stunning Superwash.)

The Pattern

The crochet pattern instructions are written out and charted. A special feature is the color-coding, which maps the portion of the chart you are working on to the color of the text you are following. The pattern testers really loved this feature.

For visual learners, there’s a video tutorial to help you understand the special techniques. While the only stitches used are slip stitch, chain, and double crochet, this is not a pattern suitable for beginners. Intermediate and experienced crocheters, however, will revel in the challenge.

If you like the images you see here, thank photographer Kellie Nuss. She did an amazing job of showing the lacy negative space between the triangles!

This is the most fun I’ve had designing something in a long time. I do hope you’ll try it yourself.

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If you are interested in learning more about continuous motifs, read my book Connect the Shapes Crochet Motifs and check out these other resources: