Ruffled Mobius Crochet Cowl

This ruffled Mobius crochet cowl is a lovely statement piece that instantly adds romance to an outfit. It combines a Mobius strip with a lacy, hyperbolic crochet ruffle for big, bold, squishy poofiness. Top it all off with a unique, wrap-around edging in a contrasting color and Hyperbole is literally the best cowl ever! (Yes, that’s hyperbole).

Hyperbole - a mobius cowl with a hyperbolic ruffle - free crochet pattern on Stitches n Scraps

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It’s all about the math!

This ruffled Mobius crochet cowl combines two math concepts. A Mobius strip, and hyperbolic crochet.

Mobius Strips

A Mobius strip is a surface that has only one side. Twisting a rectangle and then joining the ends creates a twisted loop with one continuous surface all the way around.

A mobius strip

The Mobius strip is established in the first round, creating a continuous round with twice as many stitches as you started with. This twist keeps the hyperbolic ruffle moving around the surface of the cowl. Without it, the cowl would tend to fold in half, creating a straight fold at the neckline with a layered ruffle at the edge.

Hyperbolic Crochet

In geometry, a hyperbolic plane is a surface with a constant, negative, gausian curvature. It means that every point along the surface curves in on itself at a constant rate. I won’t pretend to understand the math completely, but it’s fun and easy to create hyperbolic planes in crochet!

In hyperbolic crochet, the stitch count increases exponentially with each round. Depending on how much ruffling you want, you can double, triple, quadruple (or even more) the number of stitches by working 2, 3, 4 (or more) new stitches into every stitch.

If you are doubling your stitch count, like in this cowl, 2 stitches become 4, then 8, then 16. The rapid growth creates the curvature of the hyperbolic plane – and also makes a pretty ruffle! Adding chain spaces makes the ruffle lighter and airier, and uses less yarn too.

King Cole Yarns

King Cole generously provided the Acorn Aran and Forest Aran yarns for this project. Acorn is a lovely blend of acrylic and wool, which I used for the main section of the cowl. It comes in a variety of colorways with subtle, tweedy stripes. This color is #4954 – Juniper.

Acorn Aran Yarn from King Cole

The edging is Forest Recycled Aran. I used the same yarn in my Forest Walk Cowl pattern. It’s made from recycled fibers in a blend of wool, acrylic, polyamide and viscose. This color is #1924 – Red Brae Wood.

Forest walk twisted cowl crochet pattern on Stitches n Scraps

Reversible Edging

With the hyperbolic, ruffled edge, both sides of the fabric are visible. I struggled to find a simple, low-profile edging that looked great on both sides. So I made one up! See the full wrap-around single crochet edging tutorial:

Wrap-Around Single Crochet Edging tutorial

The wrap-around single crochet starts with a normal single crochet stitch. A slip stitch worked from back to front then pulls the single crochet up and over the edge of the fabric and locks it in place. Finally, a chain gets everything back into position to start the next stitch.

Chainless Starting Double Crochet

Double crochet rows and rounds typically start with a chain-3 that counts as the first stitch. But that chain-3 is noticeably different from the stitches around it.

A chainless starting double crochet replaces that chain-3 and resembles a typical double crochet more closely. It uses the working loop to create a faux yarn over, which you can then use to complete a double crochet in the first stitch. See this chainless starting double crochet tutorial for a closer look.

Chainless Starting Double Crochet Tutorial on Stitches n Scraps

In this pattern, the csdc stitches will give eyou a more seamless finish. But if you prefer, you can use the typical chain 3 instead.

Hyperbole Mobius Cowl

Project level Intermediate

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  • Yarn: 
    • 200 yds King Cole Forest Aran worsted weight yarn (80% premium acrylic, 20% wool. 100 g / 216 yds per skein) #4954 Juniper
    • 180 yds King Cole Forest Aran worsted weight yarn (35% wool, 20% acrylic, 20% polyamide, 25% viscose. 100 g / 328 yds per skein) #1924 Red Brae Wood
  • Hook: Size I / 5.5 mm hook or size needed to match gauge
  • Notions:
    • Scissors
    • Tapestry Needle

Project Level

Intermediate: Mostly double crochet and chains. Special stitch for edging involves working from back to front.


Approximately 26 inches diameter around the middle x 7.25 inches tall


10 dc = 4 inches

3 mobius dc rounds (1 dc on each side of center – each round is 2 dc tall) = 4 inches

Abbreviations used

This pattern uses US terms.

  • ch = chain
  • csdc = chainless starting single crochet (see Special Stitches)
  • dc = double crochet
  • rnd = round
  • RS = right side
  • sc = single crochet
  • sk = skip
  • sl st = slip stitch
  • sp = space
  • st(s) = stitch(es)
  • wasc = wrap-around single crochet (see Special Stitches)
  • yo = yarn over

Special Stitches

Chainless Starting Double Crochet (csdc): Pull working loop up to the height of a dc. Hold the loop in place, and in a counterclockwise motion, twist your hook around the loop, creating a “yarn over”. Holding both loops in place, insert your hook into the specified stitch, yo and pull up a loop.

3 loops on hook for csdc

(YO and pull through 2 loops on your hook) twice, just as you would finish a normal double crochet. Csdc counts as a dc in stitch counts at the end of rounds. (See Chainless Starting Double Crochet tutorial here).

If you prefer, you can replace the csdc wherever it appears with “ch 3, counts as dc” instead.

Wrap-Around Single Crochet (wasc): Sc in indicated st or sp, insert hook from back to front in same st or sp, yo and pull through st/sp and through loop on hook (backwards sl st made), ch 1.  (See wrap-around single crochet tutorial here)


Join rnds where indicated with a sl st in first st of the rnd. Do not turn.

Mobius Strip

Foundation Chain: With A, ch 67.

Rnd 1:

Csdc in first ch, dc in each remaining ch across.

Twist work once so that first stitch of rnd is upside down. Bring ends together to work into bottom of first st.

Dc into bottom of first stitch

Dc in bottom of first st and each st around, join in top of first st of rnd. (130 dc)

Use starting tail to sew the gap closed at the foundation chain.

Join and sew center of mobius strip closed with tail

You now have a mobius strip with the Foundation Chain at the center.

Rnd 2: Csdc in first st, dc in each remaining st around, join. (130 dc)

Hyperbolic Crochet Ruffle

Rnd 3: Csdc in first st, ch 1, (dc, ch 1) in each remaining st around, join, sl st in first ch-1 sp. (130 dc, 130 ch-1 sps)

Rnd 4: (Csdc, ch 1, dc, ch 1) in first ch-1 sp, sk next dc, [(dc, ch1) twice in next ch-1 sp, sk next dc] around, join, sl st in first ch-1 sp. (260 dc, 260 ch-1 sps)

Rnd 5: (Csdc, ch 1, dc, ch 1) in first ch-1 sp, sk next dc, [(dc, ch1) twice in next ch-1 sp, sk next dc] around, join, change to B, fasten off A. (520 dc, 520 ch-1 sps)

Wrap-Around Single Crochet Edging

Rnd 6: Ch 1, wasc in first st, wasc in next ch-1 sp, (wasc in next st, wasc in next ch-1 sp) around, join. (1040 wasc)

Fasten off and weave in all ends.


Chart does not show the twisting of the first round to create the mobius strip. Please follow written instructions for that.

Hyperbole cowl chart
Click image to expand

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Hyperbole - a mobius cowl with a hyperbolic ruffle - free crochet pattern on Stitches n Scraps

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I hope you enjoyed this mobius cowl pattern with a hyperbolic crochet ruffle. A downloadable pdf of this pattern is available on Ravelry for a small fee. The fee for the pdf format offsets the advertising revenue lost when you print or download the pattern rather than viewing it online.

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