My featured-artist display at JMM 2026 in Washington DC. Four of the works are hanging on a zig-zag of beige, custom-cut mats, and the fifth is on three black jewelry stands. All pieces were accepted into one or more juried exhibits at JMM or Bridges in the past decade. The blue knitted wall hanging, second from the left, is the solo piece that was accepted into this year’s exhibition.

A closer view of the first two panels of the folded mat backing. The three pieces were 28 inches tall and 14, 28, and 28 inches wide, which is bigger than it sounds when you’re carrying them. On the left is Fundamental Frieze Scroll II from 2018, a tan knitted wall hanging which was the precursor for the new piece to its right. That new piece, The Fundamentals of Lace, is knitted in blue on smaller needles but is both wider and taller than the older work. Both wall hangings are composed of the same fundamental region, a small lace motif in a lambda or Y shape, and both have colored beads embedded in the fabric to mark the symmetries. For more details, go to the following post for the online catalog links.

A close up of the rightmost mat panel and the jewelry set. As before, for more details you can follow the catalog links in the following posts. The last mat panel has two knitting wall hangings suspended from pins at the top of the panel. To the left is Float Free, Bumblebee, a wall hanging in two-color mosaic knitting with yellow and black yarn. Like the two pieces in the previous photo, the knitted fabric is rectangular and lashed to dowels at the top and bottom. The fabric is divided into horizontal and vertical strips with different repeating abstract designs. On the right of the mat is Redistribution, a wall hanging that has the overall shape of an hourglass whose top segment is shorter than the bottom segment. The upper portion is fan-shaped, with a network of dark purple stitches over a background of pale green stitches. The lower portion is flared like a trumpet and juts away from the wall, with a network of light purple stitches on a background of dark green. To the right of the folding backdrop is Map Coloring Jewelry Set, the oldest artwork in this display. A bead crocheted necklace with pendant, a bead crocheted bracelet, and bead woven earrings in eight matte colors with gold accents hang on a black necklace form and black bracelet and earring stands. This jewelry set won a prize in the JMM 2015 exhibit, and now and then, I still wear it.

#mathart #mathknitting #JMM2026

This year, the math art exhibition at the Joint Mathematics Meetings invited me to be a featured artist, giving me the chance to assemble this mini-retrospective of my knitted and beaded work. Links to the catalog entries are in the following posts.

🧶 #knitsky ☺️

The catalog photo of Fundamentals of Lace, a knitted wall hanging. The piece is a rectangle of blue knitted lace lashed to wooden dowels at the top and bottom. The fabric has white, yellow, and red beads knitted into the lace. The rectangle is divided into a 3 x 3 grid of different lace designs, and each section has its own pattern of colored beads that mark the symmetries of the design. The white beads, which are always in vertical or horizontal lines, mark the axes of reflection (mirror) symmetries. The yellow beads (also in vertical or horizontal lines) mark the axes of glide reflection symmetries. The red beads, which are slightly larger and more spaced out, mark centers of rotational symmetry.

Fundamentals of Lace after blocking and before attaching to dowels, lying flat on a wooden deck. Each of the nine lace designs is made up from smaller lace motifs arranged in four rows and six columns. Disregarding any beads, the motif in the upper left corner of each design is identical, a rectangle with eyelets along one diagonal and half of the other diagonal forming a lowercase lambda. The part of the motif under the lambda is an eyelet mesh, while the regions above and to the left are solid stockinette. The rest of each design consists of the same motif in various orientations, some like the original, some flipped vertically, some flipped horizontally, and some rotated by 180°. Mathematically, the motif is a “fundamental region” for the design; hence, the title of the work.

Fundamentals of Lace, pre-blocking. The lace is rumpled and uneven, and the lines of beads are much wobblier than in the finished work. Algebraically, we can prove that there are exactly nine possible symmetry structures for a design in a non-square rectangular grid repeating in two directions. The structures are expressed by the beaded markings: for instance, the middle panel gives an example of a design with no 180° rotational symmetries that has both reflections and glide reflections, and any repeating design that has evenly spaced, parallel symmetry axes that alternate between reflections and glide reflections and nothing else except translations (just sliding the design without twisting or flipping) has the same abstract symmetry structure.

#ShowMeYourKnits #knitterschoice

Fundamentals of Lace, 2025: the newest #mathart I’m exhibiting at the Joint Math Meetings next week. Details (like the allusion in the name) are through the link and in the alt text.

🧶 #knitsky #mathknitting #symmetries

gallery.bridgesmathart.org/exhibitions/...

A closeup of a blue knitted lace artwork with embedded glass beads. The section shown is divided into four rectangles of lace by strips of garter stitch, and each rectangle has its own repeating lace design. The beads form white lines, yellow lines, and red dots in various configurations. If you’re curious about the underlying math and don’t want to wait until I post the finished artwork, look up my Fundamental Frieze Scroll artworks, which were the precursors to this piece.

#ShowMeYourKnits

My current #WIP is a #mathart exhibition piece that I’m still keeping mostly under wraps, but here’s a sneak peek. The knitting is nearly complete; the blocking and mounting will take a few days on their own.

🧶 #knitsky #mathknit #mathknitting #symmetries

Jasmine Long (at the time a student at the college where I teach) wearing a boxy garter stitch cardigan with bright mosaic color work on the lower body and sleeves. The pattern is called Seven Peaks. The main color is a light/medium blue, and the color work sections consist of seven strips of two-color decorative patterns in pairs of the main color, orange, yellow, and magenta. The colored bands on the body run from mid-chest to hem, and the coordinating thinner bands on the sleeves start a couple of inches below the elbows and extend to the cuffs. The textured button band has eight pearly white buttons, one in each two-color band and one just above them.

Another image of Jasmine Long in the Seven Peaks Cardigan. Here, she is buttoning the top button (or more likely miming that) to better show the designs on the sleeves. From the top to the bottom of the sweater, the colored bands on the body and the sleeves are blue and orange, orange and yellow, yellow and magenta, magenta and orange, orange and yellow, yellow and magenta, and magenta and blue. In each set of bands, each of the seven designs represents a different one of the seven possible frieze groups, which are the different types of symmetry that patterns that repeat in a single direction (horizontally here) can present.

Jasmine Long in a side view in the Seven Peaks Cardigan, smiling, with her left hand in her hair and her right arm hanging down. Both Jasmine and the photographer, Justin Forman, were very gracious with their time and their willingness to experiment with different poses and camera angles. This version of the cardigan was designed for a math fashion show, and so I kept it simple, but the version I made for myself has pockets! Working those in without disrupting the color patterns was a fun challenge. Assuming I ever manage to publish a pattern, I’ll definitely include the pocket option.

#ShowMeYourKnits

Some year, I will finish tweaking/writing the pattern for this #garterstitch mosaic cardigan featuring the seven frieze groups and have it test knit. 😬😳

Photos by Justin Foreman, modeled by Jasmine Long.

🧶 #knitsky #mathknitting

gallery.bridgesmathart.org/exhibitions/...

Linear Lace in Burgundy, 2017. A rectangle of knitted lace in burgundy red yarn hanging from a wooden dowel. The main section of the knitting is divided into two rows of three tall rectangles each separated by garter stitch borders. Inside each rectangle is a different repeating lace design of eyelets and nupps (small bobbles featured in Estonian lace). There is a seventh lace design that forms a border at the bottom of the wall hanging. While the designs above it repeat vertically, the border design repeats horizontally, for reasons related to the symmetry groups of the seven designs.

And of course, being me, I eventually mathed it up. Here is Linear Lace in Burgundy from 2017, one of my earlier artworks representing all seven frieze groups in knitted lace. I designed the lace patterns heavily based on what I learned from Nancy Bush.

#mathknitting #knitsky 🧶

Fundamental Frieze Scroll I, 2018. A rectangle of knitted lace in teal yarn bound to wooden dowels at the top and bottom edges. The lace is divided into seven regions by garter stitch borders; one runs across the top, and the others are arranged in two rows of three. The lace is decorated with white, yellow, blue, and red beads. The lines of white beads are reflection axes, the lines of yellow beads are glide reflection axes, the blue beads are centers of 180° rotations, and the red beads are registration marks for translation symmetries.

Fundamental Frieze Scroll II, 2018. A rectangle of knitted lace in brown yarn decorated with colored beads and bound to wooden dowels at the top and bottom edges. The configuration is similar to that in the smaller Fundamental Frieze Scroll I, and the color coding of the symmetry axes, centers, and registration marks is the same. However, this wall hanging is larger, and the lace motif that makes up the seven designs is more elaborate than in the first scroll.

More #ShowMeYourKnits #lace #mathart: Fundamental Frieze Scroll I and II, 2018. Each knitted wall hanging shows all seven frieze symmetry types built from a simple lace motif. The symmetries are marked with knitted-in color-coded beads.

🧶 #knitsky #mathknitting

faculty.smcm.edu/sgoldstine/g...

A blue Linear Lace shawl hanging over beige fabric on a deck railing. The triangular shawl is draped so that the middle of the triangle falls down more or less flat while the ends are loosely folded to let the left and right corners hang down the sides. Seven different repeating lace patterns run up the right side of the triangle.

The blue Linear Lace shawl draped over an extremely patient blonde cockapoo (Kiko) lying on a deck. The left side of the shawl is bundled up behind the dog, while the right side swoops over her body and stretches out like an angel wing. Kiko is gazing softly over her shoulder, as if thinking, “Why does she keep doing this to me?”

The cover of MAA FOCUS, Newsmagazine of the Mathematical Association of America, Volume 39 Number 3, June/July 2019. The background image is a closeup of the seven lace designs in the Linear Lace shawl from the previous images.

#ShowMeYourKnits #lace, you say? 😀

Well, there’s the #mathart lace shawl I designed, Linear Lace. It shows all seven types of frieze symmetries, and proceeds are donated to @awm-math.org.

🧶 #knitsky #mathknitting

www.ravelry.com/patterns/lib...

The Double Knitting Groups (2016): a square of double knitted fabric showing a 3 x 3 grid of nine different designs. Each design features one of three motifs: spiral scrolls (these designs are on the diagonal from upper left to lower right); vines (below the scrolls and in the upper right); and hearts (the remaining three squares). In each design the motifs are teal and the background is beige. The nine design squares are outlined in teal.

The back side of The Double Knitting Groups. Compared to the previous image, everything is mirror reversed and color swapped: what is teal on the front is beige on the back, and vice versa.

I also made a wall-hanging version of the Crystalline scarf for math/art exhibitions. The yarn here is much thinner, and I knit The Double Knitting Groups on size 00 needles.

gallery.bridgesmathart.org/exhibitions/...

#mathknitting #JMM2017

Crystalline: a double-knit scarf with nine decorative designs in light blue and chocolate brown. The scarf is folded into a sideways Z shape, showing the front side (blue background, brown motifs) of six of the designs and the back side (brown background, blue motifs) of the other three. Starting from the upper left, the designs use spiral scrolls, vines, hearts, spiral scrolls, vines, hearts, spiral scrolls, vines, hearts. The scarf is resting on a brick walkway where the bricks are in the herringbone tiling. The bricks have the same symmetry group as the first vine design.

The brown and blue Crystalline scarf draped over a wooden signpost painted yellow with attached wooden arrows in yellow, green, and pink. The most prominent attachment is a pink arrow with the word “Community” painted on it in white letters outlined in black. Underneath that is the yellow piece of wood with the scarf dangling from the right end. This was the old signpost to Carrie Patterson’s Yellow Door studio, as shown by the yellow arrow with a black-and-white image of a door on it.

#ShowMeYourKnits, love and #hearts. As part of my mission to smuggle math into people’s lives, I designed a symmetry-group scarf FREE pattern for @knitty.com. I constructed the nine patterns with three motifs: scrolls, vines, and hearts.

knitty.com/ISSUEdf16/PA...

🧶 #knitsky #mathknitting

A Tree for Virahanka, 2021. A knitted wall hanging in the shape of a Japanese paper fan, with spirals of copper wire visible at the three corners. The fabric consists of a tree-like branching of dark green stitches on a beige background. The forks of the branches, which make the tree spread out into the fan shape, happen at eight different tiers going upwards from the trunk. The tiers get farther and farther apart as you go up the tree. At each height, the total number of branches is a Virahanka number, also known as a Fibonacci number, all the way up to the 55 branches at the top.

Virahanka’s Thoughts Overflow, 2021. This wall hanging, featuring a web of light grey stitches on a dark blue background, has the same branching structure as A Tree for Virahanka, with two key differences. Here, the grey lines branch downward instead of upward. Also, the tiers where the forks occur are evenly spaced, which makes the surface a flared, half-trumpet shape instead of a flat fan because the width of the knitted row grows faster as you go down from the top. The copper wire supporting the bottom is curved so that the knitting juts out, away from the wall. The copper spirals at the bottom corners are mostly hidden behind the fabric, but the knitting hangs from a large copper spiral at the top.

Redistribution, 2023. Imagine the upward fan of A Tree for Virahanka and the downward half-trumpet of Virahanka’s Thoughts Overflow, but the single column of the tree trunk connects to the top of the downward overflow, and you more or less have this work. The flat top section has dark purple branches on a pale green background, and the flared bottom section has light purple branches on a deep green background. While the previous two artworks have the same height as each other, here the two sections have the same area. Consequently, the bottom flare is around double the height of the upper fan. Both halves go to 34 branches at the outer ends.

My first series of branched brioche #mathart, 2021–2023. A Tree for Virahanka, Virahanka’s Thoughts Overflow, and Redistribution. More at faculty.smcm.edu/sgoldstine/g...

Virahanka wrote about 1, 2, 3, 5, 8, 13, … centuries before Fibonacci mentioned it in passing.

🧶 #knitsky #mathknitting

The cover of a magazine, with a photograph of a hanging sculpture, a cluster of flared surfaces knitted in red and yellow yarn and mounted on copper wire. The title text is “MAA Focus: Newsmagazine of the Mathematical Association of America.” This is Volume 44, Number 6, the December 2024/January 2025 issue.

My knitting is on the cover of Focus! (Déjà vu: my first Instagram post was the other time this happened.) Thanks to Edmund Harriss for featuring my artwork, Uniform Syncopation. More info at faculty.smcm.edu/sgoldstine/g....

(Ah, links that link!)

🧶

#mathknitting #mathart #knitsky