Pi Shawl (Elizabeth Zimmermann)
A Pi shawl is a circular shawl based on Elizabeth Zimmermann's Pi Shawl Formula: stitches double at intervals of pi (3.14...) — at rounds 4, 8, 16, 32, 64, etc. The mathematics produces a flat circular shawl that grows organically.
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The Pi formula
Cast on a small number of stitches (typically 9). Knit 3 plain rounds. Double the stitch count (now 18). Knit 7 plain rounds. Double again (36). Knit 15 plain rounds. Double again (72). The plain-round count doubles between each doubling round.
Why it stays flat
The mathematical relationship between circumference and radius (the constant pi) means that doubling the stitch count at the right intervals produces a flat circle. Done correctly, the Pi shawl lies perfectly flat with no cupping or ruffling.
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Lace placement
The plain round sections between doubling rounds are perfect canvases for lace patterns. Each section can have a different lace pattern, with the doubling rounds providing natural transitions.
Casting on
Use Emily Ocker's circular cast on for the closed centre. The 9-stitch cast on grows into a stable circular base that supports the rest of the shawl.
Abbreviation reference
| Abbreviation | Meaning |
|---|---|
| CO | cast on |
Tips
- Use Emily Ocker's cast on for the cleanest centre.
- Plan lace patterns to fit between doubling rounds.
- Block aggressively in a circular shape to set the geometry.
In depth
The Pi shawl is one of Elizabeth Zimmermann's most enduring contributions to hand-knitting. The mathematical approach to circular shawl construction transformed what had been a complex calculation into a simple formula that any knitter can apply, and the result is a flat circular shawl that has become one of the iconic shapes in modern hand-knitting.