Free Knitting Patterns inspired by Mathematical Concepts including Pi, the Fibonacci sequence, Symmetry, fractals, topology, and more. Updated 6/14/24
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.
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Free Patterns
1 2 3 Knit Numbers
These knitted numbers from 0 to 9 are perfect for education play toys for children, for birthday decorations, and more. Knit flat. Size Height: 14 cm / 5.5”. Designed by Libère tes mailles. Worsted weight yarn.
Greater Than Less Than Mitts
Inspired by the mathematical or coding symbols, these fingereless mitts feature a simple lace pattern that is very easy to work. Designed by Quirky Bird Knits. DK weight yarn.
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.
- Get the free knitting pattern
- Get Elizabeth Zimmermann’s Knitter’s Almanac with the orignal pi shawl patterns on Amazon (Paper, Kindle, or Hardcover)
- See more Pi Shawl Knitting Patterns
Pythagorean Triple Wrap
Rectangular shawl featuring mitered corners, textures, cables, and lace with a construction that shows how different geometric shapes join together to form another geometric shape inspired by the basic mathematical concept “Inscribed Square in Right Triangle”. Great stashbuster! Designed by Naurid Kashpia Senjuti for Knotions.
Fibonacci Cowl
2-color, reversible infinity scarf 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. Both colors fall into an attractive arrangement, found often in nature, starting with one color and ending with the second color. (A Fibonacci sequence is "a series of numbers in which each number is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc."). Designed by Diane L. Augustin. Aran weight yarn.
Fibonacci Barbie
These fashion doll dresses are more than pretty outfits. They are designed using the mathematical Fibonacci sequence and are great for inspiring interest in mathematics in doll-lover and knitters alike. (A Fibonacci sequence is "a series of numbers in which each number is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc."). Designed by Woolly Thoughts. DK weight yarn.
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
Anamorphic Fibonacci Socks
Stranded socks with a design using a Fibonacci sequence in a trick perspective. (A Fibonacci sequence is "a series of numbers in which each number is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc."). 3 sizes. Designed by imawale imawale. Fingering weight yarn.
Borromean Rings
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.
- Get the free knitting pattern
Get Sarah-Marie’s book Making Mathematics with Needlework on Amazon (Kindle or Hardcover)- See more Necklace Knitting Patterns
Equal Socks
These socks feature colorful equal signs in stranded colorwork, symbolizing mathematical concepts or equality or just a striking pattern. Great use for scrap yarn. 3 sizes. Designed by jewelandarlin
Binary Love Heart Hat
Knit a secret message in your hat. The stripes on this beanie spell out the word LOVE in Binary Alphabet and has an optional heart that can be omitted by just knitting or purling across the rows that feature the pattern. 2 Sizes - Fitted or Slouchy. Great gift for loved ones in tech or to share your feelings in what looks like an ordinary striped beanie. Designed by Alyson Smith. DK weight yarn.
More Free Patterns
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
Celestine Dodecahedron
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 weight. Pictured project by allincaps who had some notes
- Get the free knitting pattern for original sport weight versio
- Get the free knitting pattern for fingering weight version
- See the Ravelry page
- Get the recommended Berroco Sox yarn at Amazon
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
Crystalline Symmetry Sampler Scarf
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.)
- Get the free knitting pattern
- See the Ravelry page
- See the book Making Mathematics with Needlework: Ten Papers and Ten Projects on Amazon
- Get the recommended Lana Gatto VIP yarn on Etsy
- See more Colorful Scarf Knitting Patterns
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
Pi Beanie Hat
Pictured project by bleusheep
- Get the free knitting pattern for the Math Geek Hat designed by Yarntherapy
- See more Pi Day Knitting Patterns
Sierpinski Fractal Beanie
This hat features colorwork based on the Sierpinski triangle fractal. Options are included for 2 types of crown. DK weight yarn. Designed by Catherinemaths and Mathskath
Fractal-Shawl Mandelbrot
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. Pictured project by SINessi
Math Pencil Case
This zippered bag is decorated with mathematical symbols including pi.
Download the free knitting pattern at Ravelry
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
Binary Scarf
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.
Binary Baby Blanket
Double knit baby blanket with alphabet in binary code. Designed by Miranda Humphries
Patterns for Purchase
Fractal Shawl
Shawl or scarf knit with fractal structure. Fractals are geometric shapes that repeat their overall shape in the small details. Frattali is a large stole worked in the round, super easy to knit, and the fun fractal structure makes it interesting to knit and wear. Using yarn with long color changes accentuate the shape. Designed by Martina Behm. Perfect gift for math lovers!
Cushy Numbers
Ten patterns for knitted cushion covers and two crochet patterns illustrating mathematical concepts. Examples: Square to Eternity (top right) - Triangles are added to create a new square. Each new square is double the area of the previous square. Have It All Ways (row 5, right) - All the permutations of four colours. Wreck Tangled (row 3, right) - Each rectangle has the same area and the total of their areas is the same as the area of the background. Designed by Woolly Thoughts.
See more pics and get the ebook on Etsy
Double Base Blanket
This geometric design is a representation of binary numbers using simple garter stitch, using any yarn and needles. Make it any size from baby blanket to king-size bed. It can be made in two or six colours in any weight yarn. The design is by mathekniticians Pat Ashforth and Steve Plummer who include an explanation of the binary numbers represented.
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.
Fibonacci Bunny
Fibonacci Bunny is a cute whimsical toy that makes use of the Fibonacci Sequence for the stripes.Fibonacci Bunny is 14 inches tall. Designed by Julie L. Anderson. Pictured project by giraffadae
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.
- Get the Knitter’s Almanac on Amazon (Paper, Kindle, or Hardcover)
- See some free variations of the Pi Shawl
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.
