Math Inspired Knitting Patterns
Knitting Patterns inspired by Mathematical Concepts including Pi, the Fibonacci sequence, Symmetry, fractals, topology, and more.
To get the knitting patterns, scroll down the page to the individual pattern you want and click on the link to that pattern.
These patterns are not my designs but links to other designers who have generously shared their patterns. If you have questions about how to knit a specific pattern, please contact the designer directly.
All links on this site are for informational purposes, but please note that some links are to affiliate sellers that pay me a small commission on purchases.
Free Knitting Patterns
EZ 100th Anniversary PI Shawl: Camping
This shawl by Mwaa Knits is a tribute to Elizabeth Zimmermann who developed an easy, versatile, and innovative idea for creating circular shawls using the geometry of Pi–the relationship between a circle’s circumference and its radius– with just 6 shaping rounds. This tribute design was published in 2010 in honor of the 100th anniversary of her birth on August 9th, 1910 (8/9/10). Modifications to Elizabeth’s original design have been applied so that the lace design stitch repeats and the number of rounds are multiples of 8, 9, and 10 (the numbers in her birthday). The camping theme to the lace patterns is in honor of Elizabeth’s love of camping.
These entwined rings, inspired by mathematical concepts, can be worn as a cowl, necklace, or headband. If knit flat and small, they even make a baby toy. Borromean rings consist of three circles in which no two of the three rings are linked with each other, but nonetheless all three are linked. Designed by sarah-marie belcastro and Madison Stuart. Pictured projects by smbelcas, dmwoodman, Animae424, and smbelcas again.
Julia Fatou Fractal Potholder or Pillow Cover
This double knitting pattern was inspired by the fractal Julia0bb by Adam majewski, a combination of a Fatou set and a Julia set calculated with a computer program. Two versions: a small and a larger one, 45 cm x 45 cm for 40 cm pillow. Designed by Lina Wolf
A dodecahedron that can be used as a unique stuffed toy or holiday treetopper. Great stashbuster.Designed by Norah Gaughan. Versions for sport weight and fingering / sock weightPictured project by allincaps who had some notes There is also a video at Interweave.
Golden Mean Mitts
These fingerless mitts feature the golden mean with spiral on the top and on Fibonacci numbered stripes on the palm. These mitts depict the classic geometric representation of the golden ratio. From Wikipedia: Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Designed by Buús-Zsohár Anna
This double-knit scarf designed by a mathematician knitter Susan Goldstine to demonstrate 9 of the twelve possible plane symmetry structures described by mathematical artist Mary D. Shepherd in her book Making Mathematics with Needlework: Ten Papers and Ten Projects . (A more detailed explanation is available on the pattern page at Knitty.)
Summation of i Mitts
These fingerless arm-warmers have stripes that conform to the formula for the summation of i (between 1 and 9) – the formula used to compute the summation of the integers between 1 and 9. This formula is n(n+1) /2. So the summation of 1 through 9 would be 9 (9+1)/2 = 90/2 = 45. The mitts have 9 blocks of 10 for each of the integers and each block divided in 2 stripes with increasing by 1 row in one color and decreasing in the other color to represent the integer. Adding the rows of each color will give you the summation.2 sizes. Designed by Tasia Block
Klein Bottle Hat
This hat is a folded representation of the Klein bottle that’s a atwisted torus (donut) in the same way that a Möbius Strip is a twisted loop so it has just one surface. Designed by Marie-Christine Mahe for Knitty. Pictured project by TheresaMarie1972
Fibonacci Cables Hat
This clever beanie features cable in heights that change following the Fibonacci sequence (going backwards from 21 since the hat is knit from the bottom up). Child and Adult sizes. Designed by Maghouin Beg
Lina Wolf’s fractal wrap / shawl / scarf was designed to honor Benoît B. Mandelbrot who developed fractal geometry and the Mandelbrot set that is partially pictured in this double knit shawl. Lina’s original design included Mandelbrot’s name.
The perfect gift for the tech lover in your life, this scarf incorporates binary code into stranded colorwork knit as as a tube so the reverse is hidden. You can knit random 1s and 0s or use a binary translator to create a message for your scarf like “I love you” or the recipient’s name. Ravelrers have adapted this pattern to hats, mitts, cowls, baby clothes, and more. Designed by by Christine Dumoulin for Knitty Pictured project by Neetstoo who knit the names of her family in binary in her scarf.
Mathematical Underdogs Coffee Coasters
6 coasters including Pi, Phi φ (golden ratio), Zero 0, and (not pictured) Epsilon ε (a positive number tending toward but never reaching Zero), e and sqrt(-1). Designed by Lina Wolf. Pictured project by helenbee21
Patterns for Purchase
Making Mathematics with Needlework
This book by Sarah-Marie Belcastro and Carolyn Yackel explores the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch, and quilting). Includes patterns and projects including knitting instructions for Pillow of Braid Equivalence, Hyperbolic Baby Pants, Algebraic Socks, Torus, and Bi-Directional Hat.
Original Pi Shawls or Blankets
Elizabeth Zimmerman first published her easy, versatile, and innovative idea for creating circular shawls in 1987. Her recipe used the geometry of Pi–the relationship between a circle’s circumference and its radius — to create circular shawls containing only six shaping rounds that makes it easy to add incorporate many lace designs, as many knitters have done. Her original design included 2 patterns – a basic design and one with floral and diamond lade motifs. Pictured projects by rubycat who added extra repeat of 48 row section and a different lace border, and yarnstormer. Included in Elizabeth’s book, The Knitter’s Almanac.
The Fibonacci Cowl Class is a 2-color, reversible cowl that can be worn as a loop, doubled as a cowl and also pulled up to be a hooded scarf. The pattern harmoniously blends two colors using the Fibonacci numbering sequence in the row count. 8” wide x 60” in circumference. Designed by yarnhappybeadhappy
Dragon Curve Fractal Scarf and Hat
The Dragon Curve Fractal is the fractal featured in the chapter headings for Jurassic Park by Michael Crichton and is repeated in this doubleknit scarf and hat. Designed by the Nifty Knitter
Fibo-optic Afghan / Wall Hanging
Fibo-optic uses the Fibonacci Sequence in two directions, in each of the three dimensions, to give the illusion of a large flying cube.
This design by woollythoughts is nowhere near as complicated to make as you may think. If you can knit garter stitch, you can do it.
Mr Pythagoras and Mr Fibonacci Puppets
Mr Fibonacci wears a robe designed to show his well-known sequence, in two directions. He also wears a hat showing the same pattern of numbers. Mr Pythagoras wears an example of his theorem on his front. These were designed with adults in mind but are small enough to also be used by a child. Designed by Woolly Thoughts
Terry is a knitting late-bloomer, learning to knit as an adult from Internet tutorials, because she wanted a craft that was useful, fun, and portable. Knitting hats for cancer patients inspired her to design her own patterns—available for free at her blog, intheloopknitting.com. Terry met her husband Ken at a science fiction convention and moved to the Kansas City area to be with him more than 30 years ago. Terry supports her yarn stash by creating websites and other digital media. Terry firmly believes in Knitting in Public—it's a great conversation starter!