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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.

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 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.

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/...

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I love the way the #ShowMeYourKnits prompts encourage me to look at my older pieces with fresh eyes, so for #knitterschoice week I’ve chosen the newest finished thing I’ve got. Here’s my #Tessasweater, in yarn from @thebluebrick.bsky.social and #plymouthyarns. #knitsky

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My Vitamin D cardigan in progress.  The sweater is knit from the top down in one piece. One sleeve, knit flat and still to be sewn shut, juts out to the left. The top of the other sleeve, the back, and both fronts are on circular cables, with stoppers screwed to the ends on the back and fronts and the size 2.5 needle tips ready to start the second sleeve.  The top of the cardigan is all bright green, but the left sleeve fades through pink into maroon.

My Vitamin D cardigan in progress. The sweater is knit from the top down in one piece. One sleeve, knit flat and still to be sewn shut, juts out to the left. The top of the other sleeve, the back, and both fronts are on circular cables, with stoppers screwed to the ends on the back and fronts and the size 2.5 needle tips ready to start the second sleeve. The top of the cardigan is all bright green, but the left sleeve fades through pink into maroon.

#ShowMeYourKnits #knitterschoice

… and THERE’s the gradient! On to the second sleeve…

The shop.thebluebrick.ca sweater kit is in Blossom. I’m less certain of how the gradient yarn will work in the body, where it meets Vitamin D’s short rows, but I’m looking forward to finding out.

🧶 #knitsky

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A close up of the Vitamin D cardigan I’m currently knitting after I found a truly implausible error. My fingertips are at the top, holding down the cast-on edge to show the problem. In the middle of what should be a line of regularly spaced yarn-over holes, one hole seems to be missing.  On closer inspection, I realized that at some point when I was returning some stitches that had come off the needle, I must have accidentally let the top edge run through the “missing” eyelet.  I debated just leaving it since I was well past this point, but instead took a deep breath and ripped back a few dozen rows to fix it.  Definitely the right call.

A close up of the Vitamin D cardigan I’m currently knitting after I found a truly implausible error. My fingertips are at the top, holding down the cast-on edge to show the problem. In the middle of what should be a line of regularly spaced yarn-over holes, one hole seems to be missing. On closer inspection, I realized that at some point when I was returning some stitches that had come off the needle, I must have accidentally let the top edge run through the “missing” eyelet. I debated just leaving it since I was well past this point, but instead took a deep breath and ripped back a few dozen rows to fix it. Definitely the right call.

What the top of the Vitamin D cardigan is SUPPOSED to look like. There are radial grids of yarn-over increases on the fronts and the back of the cardigan, with plain stockinette wedges for the tops of the raglan sleeves. The error I had to pick out was at the top of back, where the now unobstructed top edge is curling the way unsupported stockinette does. This image is just over halfway through the increase section at the top.  As of this posting, I’ve finished this section and am knitting the first sleeve, where the color gradient kicks in.

What the top of the Vitamin D cardigan is SUPPOSED to look like. There are radial grids of yarn-over increases on the fronts and the back of the cardigan, with plain stockinette wedges for the tops of the raglan sleeves. The error I had to pick out was at the top of back, where the now unobstructed top edge is curling the way unsupported stockinette does. This image is just over halfway through the increase section at the top. As of this posting, I’ve finished this section and am knitting the first sleeve, where the color gradient kicks in.

Early in the knitting of the Summit shawl I made in 2010. The light blue shawl consists of wavy strips of stockinette with dropped-stitch ladders and big open holes between them. In the first row of holes, I managed through a lapse of attention to twist the fabric so that the bottom edge actually ran through one of the holes, but didn’t notice until I had finished the entire second row of holes. (Wine and conversation were involved.)  While ripping back to the offending twist was annoying, it did give me a good laugh.

Early in the knitting of the Summit shawl I made in 2010. The light blue shawl consists of wavy strips of stockinette with dropped-stitch ladders and big open holes between them. In the first row of holes, I managed through a lapse of attention to twist the fabric so that the bottom edge actually ran through one of the holes, but didn’t notice until I had finished the entire second row of holes. (Wine and conversation were involved.) While ripping back to the offending twist was annoying, it did give me a good laugh.

The middle of the unblocked Summit shawl. I spread out the rectangular shawl loosely and let the middle stay bunched up to show the drape and the depth produced by the curl of the unblocked strips of stockinette that undulate between the lines of drop-stitch framed holes. I will link this pattern (as well as the cardigan pattern) in a reply post. I knit this in the raw silk yarn from the pattern, in the same pale blue color.

The middle of the unblocked Summit shawl. I spread out the rectangular shawl loosely and let the middle stay bunched up to show the drape and the depth produced by the curl of the unblocked strips of stockinette that undulate between the lines of drop-stitch framed holes. I will link this pattern (as well as the cardigan pattern) in a reply post. I knit this in the raw silk yarn from the pattern, in the same pale blue color.

#ShowMeYourKnits #knitterschoice

Early in my current WIP, I reproduced a rare knitting error I last made 15 years ago: passing the edge of the knitting through a hole in the knitting. Nothing for it but to rip back and reknit. A nice reminder that spectacular missteps are part of the journey. 🧶🙃🎉

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Kitchen table with various hand knitted and crocheted items undergoing blocking and finishing. There’s a child’s blanket, a doll blanket, a lacy coaster, and some headbands.

Kitchen table with various hand knitted and crocheted items undergoing blocking and finishing. There’s a child’s blanket, a doll blanket, a lacy coaster, and some headbands.

Hello, #knitsky friends! Here’s my contribution to this week’s theme of #KnittersChoice. Here’s some projects in various stages of blocking and finishing. 🧶 #yarnparty #fiberart #knittingisresistance

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