Hyperbolic Barbie

Hyperbolic crochet has become very popular in recent years. It has been used world-wide in various coral reef projects. The world expert in the mathematics of this art is Daina Taimina.

Our latest mathematical pattern for Barbie and friends is Hyperbolic Barbie.

Hyperbolic geometry is quite complicated but you don’t need to understand it to make these simple dresses. The pattern includes three crochet dresses, three knitted dresses and two scarves. It is intended to show what happens when you repeat the same pattern of stitches over and over again, and how making one small change quickly has a dramatic effect.

• The pink frill begins with 26 stitches
• Row 2 has 52 stitches
• Row 3 has 104 stitches
• Row 4 has 208 stitches
• If you could add more it would increase to 416.

• The blue frill begins with 26 stitches
• Row 2 has 39 stitches
• Row 3 has 58 stitches (approx)
• Row 4 has 87 stitches (approx)
• The next row would have 130 (approx)
• The dark blue frill begins with 30 stitches
• Round 2 has 60 stitches
• Round 3 has 120 stitches
• Round 4 has 240 stitches
• The next round would have 480

• The cream frill begins with 30 stitches
• Round 2 has 45 stitches
• Round 3 has 67 stitches (approx)
• Round 4 has 100 stitches (approx)
• The next round would have 150 stitches (approx)

It is clear to see that the numbers diverge rapidly when the rate of increase is changed.

It is much easier to make hyperbolic frills in crochet than it is in knitting. When you crochet you only have one stitch on the hook. You can work into it as many times as want and can twist and turn the dress to make the stitches. Knitting is in a straight line and all the extra stitches have to get forced into that line. It soon becomes physically impossible to add any more.