Weavers: Relaxation, Invitation, Ornamentation

I’m in an art exhibit for the first time ever! [This is more a function of me getting in gear than anything else, but it’s exciting nonetheless.] A set of three mixed-media fiber art pieces, with sewing, embroidery, weaving, and gluing.

"relaxation" art embroidery "invitation" art embroidery "ornamentation" art embroidery

From left to right, these are Relaxation, Invitation, Ornamentation. Click to embiggen; the next larger size would have made them taller than my browser window, and I find that super annoying on other sites.

My hubby took some fantastic closeups of them that I’ll share two of:

"relaxation" embroidery detail "ornamentation" embroidery detail

These will be on display at the Upper Valley Food Co-op in White River Junction, VT, as part of their Earth Day art show. I believe they are up for three weeks starting today, and there’s a reception 4-6 PM today.

A bit on the making: The hoops are 12″, 10″, and 8″ wooden embroidery hoops painted with acrylics; two are over 12″ scrapbook paper. Each has a two-layer fabric “frame” perhaps with other fabric elements and a hanging ribbon that originated on a candy package. The webs are nylon filament sold for beading and the dewdrops are Mod Podge Dimensional Magic, a material I’d been looking for an excuse to buy and try.

The smaller spider is thread and wire (and a loop of filament leading to the hanging thread), held in place with friction and Fray-Check. The bigger one is wire and beads made rigid partially via Jewel-It embellishment glue. The wire lettering is also held in place by Jewel-It. I used steam (was going to say an iron, but that implies touching) to “block” the nylon, which shrinks it a bit but also helps it take the shape it’s pinned to when heated. That was especially important for the hanging spider, who doesn’t weigh enough to straighten the nylon itself!

Single Crochet Shaping 3: polygons

If you want to crochet a smooth disk, you should stagger the increases round to round. If they stack up on top of each other they tend to make corners. If you want something with corners, though, can you figure out how to make it without pure trial and error? In particular, if you want to make regular polygons of various numbers of sides, how do you figure out how to increase?

crochet polygons from three sides to eight

Being who I am, I began with geometry. A disk takes 6 or 7 increases around because when you increase the radius of a circle by 1 unit (i.e. by one round) the perimeter increases by 2π units, 6.28ish. We have to fudge a little, of course, since an sc doesn’t add exactly the same amount to circumference as to radius and we can only increase by whole stitches, but it works out; we are able to make disks.

For a polygon, there are two distances that could play the role of the circle’s radius: center to corner (radius), and center to edge midpoint (apothem). We have formulas that tell you how much the perimeter increases when the radius or apothem increases by 1, depending only on the kind of polygon you’re expanding.

Shockingly, I’ve decided not to go into the algebra here; you can read all about it Math Open Reference. My previous knowledge says you need 8 extra stitches for a square, and that number should be larger for fewer sides and smaller for more sides (you need more stitches to get around pointier corners). Those both matched the apothem calculation and not the radius calculation.

polygon extra stitches per round from apothem formula
triangle 10.4
square 8
pentagon 7.3
hexagon 6.9
heptagon 6.7
octagon 6.6

The apothem numbers leave a lot to be worked out: how to round, what to do when the increases aren’t a multiple of the number of sides, and whether an octagon could even be made when it called for fewer increases per round than corners. I made all six polygons more or less successfully, but they broke out into half easier, half harder.

the easier three polygons to make: triangle, square, heptagon

The easy polygons were the triangle, square, and heptagon.

Triangle: This didn’t go how I expected – I thought I would need to round up to 12 extra stitches per round, but I actually dropped down to 9. I started with 6 sc in a magic ring, and every corner got 4sc. Increases made into previous increases went into the third of the four sc.

Square: As I said, I already knew to put 3sc into the corners to make a square. I started with 6 sc, increased around, and then started making concentrated increases for corners. Increases made into previous increases were made into the middle sc.

Heptagon: Since for me, seven increases is appropriate for making a flat disk, the heptagon was straightforward. YMMV. I started with seven stitches, increased around, and then increased in the second stitch of each previous increase. To improve the point of the corners, in the last round I made 3sc into the second stitch of every previous round increase.

the three more complicated polygons: pentagon, hexagon, octagon

Pentagon, hexagon, and octagon were more difficult, but they did work reasonably well.

Pentagon: The pentagon formula called for 7.3 new stitches per round. Since five 2sc increases would add 5 and five 3sc increases would add 10, I alternated between them: start with 5 sc in a magic ring and make 3sc into each of them. Next round, put 2sc into the center of each 3sc increase; round after that, put 3sc into the second of each 2sc increase. Continue alternating, ending on a 3sc round. I did attempt mixing 2sc and 3sc increases within individual rounds, but it was a mess to keep the side lengths equal.

Hexagon: Like the pentagon, I used a combination of 2sc and 3sc increase rounds. The hexagon’s apothem number was lower and the number of increases per round higher (6 or 12) so I made two 2sc increase rounds for every one 3sc increase round. It perhaps would be even better to make three 2sc rounds per 3sc round, but I worried about maintaining the flatness of the piece. Start with 6 sc in a magic ring, make 3sc into each of them, and then make two rounds of 2sc increasing and one of 3sc. Put your increases into the second stitch of a 2sc predecessor or the middle stitch of a 3sc predecessor, and for best results end on a 3sc round.

Octagon: How can one even make an octagon if even one increase per corner leads to too many stitches around for the piece to stay flat? I suspect the best answer is to make a disk large enough to naturally hit a multiple of 8 stitches around and then do something like (sc, hdc, sc) in each corner on the last round. I wanted to try to stick to the size and methods of the other polygons (though I didn’t quite) and ended up with this: 7 sc in a magic ring; 2sc around; *2sc, sc* around. You’re at 21 stitches. Make a big jump to 32: *2sc, sc* 10 times, 2sc. Last round: sc 2, *(sc, ch, sc), sc 3* 7 times, (sc, ch, sc), sc. The chain in the middle of the last round’s increases gives it a little bit more point without adding even more extra bulk than we already have.

There you have it: all the polygons from 8 sides down rendered in crochet, for your freeform delight. I did these all in spirals and ended with a needle join in the second stitch; the ultimate perimeter would be smoother if you worked in joined rounds.

Looking back, looking forward

I realized this afternoon that I let my fifth crochetiversary (in mid-November) and blogiversary (March 31) go unremarked upon. Sometime earlier last fall was my fifth anniversary with the Sew-op, as well. It made me think about how much has changed for me in the last five years.

When I started this blog, I had just realized I didn’t want to stay in mathematics, but had no idea what my next career would be. I was a week or so away from first meeting the man who became my husband, and we wouldn’t start dating for over eight months.

2011 was incredibly productive for me, though I was still working full time as a mathematician the whole year. It was my second most prolific year by measure of entries into the catalog and third by total number of posts (popping up to a very close second if you prorate). Surprisingly little of it was older work getting blogged about retroactively – I simply did a lot.

My most productive time was when I was semi-attempting to be a professional craft designer and teacher, roughly April 2013 to April 2014. I lacked the requisite passion and grit to make that happen, and discovered I really dislike sewing to order. I had already begun web development, learning enough to modify this blog’s theme and proceeding from there. I joined my little startup in February or March of 2014 and tried to make that work.

At the beginning of last year I decided to abandon the steady, frequent posting schedule I’d been more or less maintaining. That was absolutely the right decision. The nomadic piles of stuff in my sewing room are gone now, after a little work that was worth blogging about and a lot that wasn’t. I have plans to get through more longstanding projects during this quarter of the year, which will get me all but dug out of old project plans.

After that? Next month I begin a new job. I’ll be doing web development full time in an office. Reflecting on 2011 makes me wonder how 2016 will turn out. Being on the computer all day at home makes it hard to get off the computer; working for a start-up and freelancing without succeeding financially, and then also job hunting, makes it hard to think you should ever stop working. 2016 won’t be as productive as 2011 – for one thing, I was single for the second half of that year – but I’m hoping to simply do a lot again.