Maple candy!

Having read the Laura Ingalls Wilder books as a child, it appears that I share with several friends a long-harbored ambition to make maple candy on snow!

Well, we have a snowstorm: 6 to 8 inches so far (15-20 cm), and we may get as much as a foot (30cm). Hopefully I won’t lose power; I’ve taken some pictures.

I can't take a good picture of the snow in my yard without daylight, but here's a bush right outside the door.

Advised by the top three Google hits for “how to make maple candy with snow”, we boiled half a cup of maple syrup with a tiny bit of butter up to 230 F, gathered several bowls of clean snow (but for acid rain), and ladled patterns into them, let them cool, and ate chewy candy.

That's my sister Diana in the background! I gathered, she poured.


The longer you heat the maple syrup, the harder they get; but leaving them in the snow longer made some of them a bit harder anyway.

Keeping them is tricky: I’m sticking some in the freezer on the bowls of snow, because I’m afraid melted snow may dissolve them. Oh, also, do NOT use a paper towel except for preliminary drying. Wax paper. I told Diana to deal with the last few, and she got them stuck to the towel! Later: the frozen ones are great.

Sierpinski shawl

My mother gave me a book called “Making Mathematics with Needlework” last Christmas, and I fell in love with the idea of making a Sierpinski fractal shawl. Here’s a nice picture and explanation of the Sierpinski triangle”. Basically you take a triangle, bisect the sides to cut out a smaller triangle, and then you have three triangles; keep doing it. My shawl has 5 iterations, and I crocheted it from the bottom tip up. It’s not equilateral! But it still works.

The basic pattern is this: each row increases by 1 arch. The row starts and finishes with 2 arches, which are made by chaining 5 stitches and then attaching it to the arch (or filled fan) below it by a single-crochet. The filled pieces (fans) are made by triple-crocheting thrice into the same stitch and then attaching in a similar way. I don’t like this pattern all that much because it ultimately doesn’t make triangles so much as curvy diamonds, but it worked well overall. It took me forever, though, because each row just kept getting longer! I used a variegated baby yarn of sport weight and a size G hook.

An overall view. It's about 3 feet from base to tip, but the base stretches to about 5 feet.

A closer up view. It's upside-down from the way I actually crocheted it, though.

I also learned something about the Sierpinski triangle that I didn’t know: it’s the mod 2 Pascal’s triangle. That is, it looks like this:
      1
     1 1
   1 2 1
  1 3 3 1
1 4 6 4 1

so you always add the two numbers in one row to get the number in the next row, except that you put a 0 (a hole) whenever the number is even and a 1 (filled space) when it’s odd. That way you get
         1
       1 1
      1 0 1
     1 1 1 1
    1 0 0 0 1
   1 1 0 0 1 1
  1 0 1 0 1 0 1
1 1 1 1 1 1 1 1

and so on. So you can build it from the ground up instead of cutting pieces out. Whee, math geekiness!

Potholder stitch and periodicity

Ordinarily, crocheting in variegated yarn produces alternating patterns because the crocheting goes back and forth. But when you do potholder stitch (see my earlier post) the situation is different. Each row only shows on one side, so all the rows on the same side go in the same direction. That means that a pattern will tend to be regular.

My aunt got some yarn for me to make potholders, and it’s white yarn variegated with five rainbow colors (not blue or indigo). Each white or colored section takes about 6 inches, or 3 stitches. So my 30 stitches turned out to be nearly perfect to make the yarn go through exactly one cycle per side. I thought this would mean that the potholder would have boring nearly-vertical stripes, but it turns out that the dyeing of the yarn is not quite regular enough to permit that. It’s close, but it has zany variation! Take a look.

I didn’t bother to flip my pictures this time: my computer takes all its pictures as mirror-images, which is sort of annoying, but this way it looks as if I crocheted right-handed. Shrug. ūüôā

Tangrams

tangramcrafts

I wanted to make tangrams for my school, and I discovered that lined 3”x5” index cards are perfect for making tangrams! This is because the distance from the top line to the bottom line is exactly 2.5” and the lines are 1/4” apart, so the middle line is marked.

To make tangrams out of an index card:
0. You could cut off the top and bottom outside the lines if you want, to give yourself straightedges and not get confused. Or you can do that at the end, and use another index card for a straightedge and perpendicular.
1. Fold the index card in half, to make two squares, and trace the resulting line. Draw the diagonal in one square to make the two big triangles. Make sure to check that the two diagonals meet at the center card-line, thus:

It's hard to see, but the topmost index card is showing the diagonal on the bottom, which meets the pencilled line in the middle.

It's hard to see, but the topmost index card is showing the diagonal on the bottom, which meets the pencilled line in the middle.


2. Start the diagonals in the other square, but only to the center point of that square (which, again, you can find using the index card’s middle line). Now you have the medium-size triangle.

3. Using the other index card to make a perpendicular line, draw a vertical line halfway up in the middle of the second square. Mark the same line at the top. Now you should have the square and one small triangle.

4. Draw the last diagonal from the side of the card to the midpoint of the top line, so that you have the parallelogram and the other small triangle.

I am in the Madrid Café at 45th and Sansom, Philadelphia.  The owner was happy to try tangrams.

I am in the Madrid Café at 45th and Sansom, Philadelphia. The owner was happy to try tangrams.

I also discovered a tangram alphabet, whence the title picture.

Finally, I made my own “paradox.” I’m sure this has been done and googling will reveal it; nevertheless, I invented it myself. ūüôā Having gone back to tangrams with a much more mathematically trained mind than I had as a child, I always consider the lengths of sides and parallel positions and so on, so it’s much easier to solve tangrams and to puzzle out things like that.

Wait, one of the squares has a hole in it...

Wait, one of the squares has a hole in it...

Better tapestry pictures

We’ve been making progress! There isn’t much to say about it, except that I now have a proper digital camera so you can see the results.

Potholder

I have now crocheted two versions of a Potholder Stitch Oven Mitt: one for me and my roommates, one for my father. ¬†The website with the instructions seems to have been shut down! ¬†So, the way I do it is with Sugar&Cream cotton yarn, because it’s good for high temperatures and it’s variegated. ¬†I use a size G hook, but another size would be okay.

The tricky thing is how to do a potholder stitch. ¬†You start with an ordinary chain for row 0; then, for the first row, you single-crochet only in the back loop of that row, leaving the front loops. ¬†At the end of the row chain and turn, and then single-crochet through the back loop of the first row and the remaining (front) loops of row 0. ¬†You’ve left the front loops of the first row alone, so for row 3 you use those loops along with the back loops of row 2. ¬†The overall effect is a kind of crocheting that is twice as thick and the stitches on a given side all face the same direction.

Instructions:

0: Chain 21 stitches.  Turn. 
1: Sc (single-crochet) into back loop only of row 0, 19 stitches.  Chain 1.  Turn.
2: Sc (single-crochet) into back loop of row 1 together with front loop of row 0, 19 stitches.  Chain 1.  Turn.
3-30: Continue, until you have 15 rows visible on each side.

Thumb: Do only 5 stitches for row 31; chain 1, turn. ¬†Continue for a total of 10 5-stitch rows. ¬†Then to neaten up the top, pull a loop through *both* loops of the first stitch of row 40 and the back loop of the last of row 39; pull another loop as usual for the second stitch; yarn over and pull through all three loops. ¬†So, in other words, crochet the first two stitches together but use up the front loop too for the first stitch because you won’t need it. ¬†Do the next stitch as usual; then for the third, crochet the last two together, using up the front loop of the last.¬†¬†Chain 1, turn. ¬†Crochet the first two stitches together as before, and do the third one single-crochet through all three loops. ¬†Knot the yarn, cut it.

Fingers: Go back to the other 14 stitches, and do as the thumb was.  I do it for 14 full stitches, making the thumb stick out slightly.  The original instructions have it just for 13, so the thumb can go straight up.  Anyway, do 20 rows for this (10 on each side) then decrease each row at beginning and end, so by 2 stitches and using up the extra loops, 3-4 times or until satisfied with the shape.  Finish.

Finally, you go and make another one, and sew them together on the edges except at the bottom.  I ended up crocheting them together along the edges and then turning it out, but that may not be the best way to do it.

Here’s a picture of the first one I did:

Gryphon tapestry: claws, wingtips and diagram

Elisabeth,  silkspinner and I have made progress on the gryphon tapestry!

We found a small picture of a gryphon online, scaled it up so that it was low-resolution, and traced outlines onto graph paper.  We taped enough graph paper together to make a diagram to scale, and scaled up the beginning diagram by the low-tech method of drawing in nine squares what originally was in one.  Then we used a lot of our imagination to fill in some details on the main diagram; there may be too many details to cover in the tapestry, but given what we know of the techniques of the last one we think we should be able to manage.  We have not yet had the perseverance to reproduce our single gryphon in mirror image on the other side, so we now have half a diagram taped to the back of the tapestry.  Still, it can be used!

upperdiagram

The two pictures here don’t quite fit together; my photography skills are currently limited by my cell phone’s camera.

lowerdiagramWe bought a variegated yarn for the background color, so that it varies between dull green, blue-green, and blonde.¬† We have three levels of shading for the “lion” hindquarters, and three for the eagle, as well as gold and black.¬† When weaving the dragon tapestry we had trouble finding all our threads of the right thickness, so we ended up with some five-ply threads that we had to re-ply (in pieces) into three-ply thread.¬† This time we shouldn’t have to do much of that, though the black thread will have to be divided up.

In the past week or so Elisabeth and I began weaving, leaving a gap of one bare warp thread for the divide between the two halves, and making sure the halves are woven at the same rate.¬† Today, we brought it with us to New York, and this afternoon silkspinner joined us in working on it!¬† Elisabeth started the tips of the wings today, but so far they’re hard to see because the “eagle green” color (a yarn handspun by silkspinner herself) is as dark as parts of the background.¬† Meanwhile silkspinner and I struggled through the first rows of the hind claws and tail.¬† I copied what she did, some of which you can see here:

lowerdivide1Here you can see the wood frame and warp threads where they appear in the middle of the divide.¬† Since this is the edge, the curve of the divide is especially steep.¬†¬† The overwhelming majority of the color in this picture is supplied by the variegated background thread, but towards the top you can see the bottom of the claws in gold, the lion color, and the lion-shadow color.¬† The splotch of lion to the right is the bottom scoop of the tail.¬† So far we’re at 20 rows on the bottom and 21 at the top!