Video: Circle Center

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Once you finish a book on geometry, everyone wants help. 🙂

I wound up making this short video on how to find the center of a circle for my dad.  It’s not ideal; I need a better set-up for making videos at my desk.  But the essence of it are these steps:

  1. On a given circle, find three points about 1/3 of the way around the circle, A, B, and C.
  2. Arc the distance AB center A, and BA center B, so the arcs overlap one another at two points, D and E.  Draw a line between D and E — the center will be on that line.
  3. Arc the distance AC center A, and CA center C, so the arcs overlap one another at points F and G.  Draw the line between D and E — the center has to be on that line.
  4. Point O is the place where lines DE and FG cross. That’s the center of the circle.

I hope this helps!

Geometry book: end of prep 

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I’ve been working on this hand-written book of geometry since at least 2013… maybe since 2011. There’s a total of fifty pages or leaves in it, although it’s an accordion-style Japanese album from Moleskine.  I recently started working on it again due to some recent geometry work in my life, and I’ve put in a few longish days.  The work itself is a manuscript to teach myself the material from Andrew Sutton’s book, Ruler and Compass, available from Wooden Books Press (a division of Bloomsbury).

Several years ago, it might have been early 2014, I laid out most of the remaining pages — the margins of each panel, the lines for the text, and the two or three geometry figures for each page.  For reasons passing understanding at this late juncture, I failed to lay out the last six pages of the book, or plan for the inside front cover.  The result was that I created a milestone, of sorts, in this project — the end of already-laid-out pages, six pages before the end, when I’d have to plan the remaining six pages and finish the inside front cover.

I’m now at that point.  My goal was to get here by Memorial Day weekend, and I’ve achieved that goal a bit earlier than expected.  I probably won’t be able to get back into this work until after the weekend, but I’ve made good progress.

Geometry: back to work 

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It’s been a good long while since this particular project occupied my attention and focus.  However, I’m currently motivated to finish it — or at least finish the nine pages that I already have outlined and planned.  There are six more pages that are unplanned except for the margins, which means that I have a total of fifteen pages left to write, and maybe a card or panel to put in the pocket of the book, an afterword of sorts to explain the project a little better than I did at the beginning.

What project am I talking about? This one, the geometry book that I began a long time ago practically in a galaxy far, far away.  In fact, from the earlier entries from 2013, I can tell that I was already about sixteen pages into it.  Now, I’m thirty-seven pages into it, and I have fifteen left.  I’m almost the opposite point in this project as I was four years ago.  Funny how these things circle around, right?

The current pages, #36-37

Of course today is the day that I made a mistake.  I drew out the process of comparing 1:√2, and didn’t discover my error (on the right-hand page) until I had already inked the diagram and written the explanatory text.  Always check your work in geometry before you render it in pen!

The next pages laid out (and upside down for some reason)

No matter.  I had the room to be able to describe the process incorrectly, add in A WARNING IN CAPITALS AND RED, and then offer the correction. Typical medieval manuscript at this point, really — sometimes errors creep in, and the lowly scribe has to figure out how to offer the correction clearly and legibly in less space.  I managed.

As I said, I have nine pages remaining in this project that are already laid out.  A lot of this project is me working through Andrew Sutton’s book, Ruler and Compass from Wooden Books.

Why did I return to it, though? Well, first, I’m trying to clear my desk of unfinished projects. This one has been a big one, and it’s been on my mind to complete for a while.  But for another, I recently took up the opportunities and challenges of tutoring again.  And I’m tutoring a few young people in geometry.  So this project is serving to lubricate and rub the rust off of my geometry skills. Even so, I’m finding that the knowledge of actual geometric proofs isn’t quite as useful as one might imagine.

A lot of the work that students do in geometry class these days appears to be algebra. There will be one diagram (with a note beside it to say, not to scale or not rendered accurately), and then a lot of algebraic notation, and the student is expected to work without a ruler and compassed just their brain power and maybe a calculator, to solve the problem.

Say what??

I don’t understand.

Are we teaching geometry, or geometric algebra?  It looks like the latter, rather than the former.  And I understand that teaching actual geometry is challenging, and that it involves looking at a lot of diagrams and working out a lot of constructions by hand… but heck, that’s what we do as human beings. Isn’t it?

I said to someone on Twitter today that

Screen Shot 2017-05-15 at 2.43.25 PM

pardon, I can’t figure out the ’embed tweet’ system for my server.

But that’s (more or less) true — we use our hands to instruct our brains, and vice-versa.  How do we actually learn geometry if we’re not using the tools that geometry has used for thousands of years (or reasonable electronic replacements, though I’d argue that such tools are not as good as actually using hands to manipulate a compass)?

In any case, here’s a place where abstraction often gets the best of us.  I think it’s time to bring back some actual geometry to the classroom, and not simply ask students to do it algebraically.  This is a set of skills that belongs in our students’ hands, and not just in their heads.

Sewing: Viking Bag 2 

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Remember that cute viking fabric that I made into those little drawstring bags?

I found another strip of it.  But it wasn’t enough to make into a bag, unfortunately.  I was going to have to combine it with another kind of fabric? What goes with vikings, though? How do you combine viking warriors with anything else? Floral prints?

But how about a brick wall?  If I make the bag tall enough, it will look like warriors peeking over the battlements of a tower, and that conveys the image that we’re looking for — not a bag, but a tower, not a small purse but a fortress.  It becomes a thing of the imagination, as much as a physical object.

I’d rather it was a stone wall, or maybe spiked logs, like on a rough-and-ready motte and bailey castle.  That would make sense, after all.  The vikings didn’t build too much in brick (they also didn’t wear horned helmets — not very practical in warfare, really).

No matter. I found some brick fabric, and it matches pretty nicely with the vikings.  And then I found some other fabric that sort of resembled the Lord Baltimore colors in the Maryland flag… somewhat heraldic, though not TOO heraldic… not shields with lions and snakes and so on.  That would have been a seriously lucky find, though, in an American fabric store.  In general, though, we don’t really understand heraldry’s rules, so they often get used against us — in advertising, in snobbery and class warfare, and other ways, as well.  That’s not really at issue here, though.
What is at issue, for me, is how much of Makery in schools seems to be “making for the sake of making” — that students should simply be allowed to make whatever it is they want to make, full-blown from their imaginations. I don’t know that there’s anything wrong with just letting people make what they want to make, mind you — there’s benefit to that, and real results can emerge from allowing that spark of creativity.

But I think there’s a place in Making for making with a purpose.  There’s a lot to be gleaned from making a quilt to keep a baby warm, or from making a bag like a tower for holding a bottle of wine or something similarly fragile and precious, or a bag that looks like a pencil case. There’s a place for unbridled creativity. But there’s also benefit to knowing how to do something the right way.

I mean, think about it.  In a tailor’s shop 500 years ago, an apprentice would have to work on a variety of tedious projects — sharpening scissors, ironing fabric (I can’t imagine how difficult that work was before electric irons), measuring clients (and then measuring them again when the measurements proved wrong), learning to sew straight seams. They would have made a variety of things that no one would care if they were slightly off — bags with drawstrings, bags with handles, awnings for market stalls, aprons for the shopkeepers, tool rolls for traveling workmen, sacks for flour, and similar projects.  These are a vital and necessary part of the learning of any artisanal technology, be it sewing or woodworking — the cruddy projects that no one really wants to do but that are genuinely vital to the good functioning of that sort of society.

Thirty years after my own first sewing experiences in a Home Economics class in 8th or 9th grade, I find that these skills are returning to me with some rapidity.  I’m much more skilled at whipping up a bag or an apron than I used to be, in part because I’ve trained those skills to a level of complexity and skill where it’s easier to just do it.  I’ve learned a good deal of the apprentice work of this business of sewing (maybe not everything, because every so often I encounter a challenge that I have to go to a YouTube video to solve).

But that’s what the Walking Foot was about.  That’s what making potholders was about. These aren’t “stupid projects” but the foundations of the craft.  In carpentry it’s probably smoothing boards; in bookbinding it’s folding and punching pages; in fabric it’s making potholders and bags.

What are the foundations of your craft?  When did you feel like you went from being an apprentice to being a journeyman or journey woman? When did you become a master of your art form?

Sewing: potholder

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In almost any quilting project, it’s always the case that you wind up with one or two or six extra squares. It’s basically a byproduct of mathematics —  x number of squares will only fit into y number of columns and z number of rows.  But the cut-and-sew process of generating the squares — this one was the result of piecing together six strips of 2.5″ cloth into two units of three strips each — one arranged blue-green-blue; the other arranged green-blue-green. Those were then sliced into strips 2.5″ wide, and then reassembled into 3×3 grids — all the while picking up noise and getting smaller along the way, because I’m apparently messy like that.

Yesterday, I bought a walking foot for my sewing machine, and I was delighted with the results.  Posting about it on social media brought me a host of discussions about replacing my store-bought 100% polyester bias tape with hand-made 100% cotton bias tape.  I said I didn’t know how to do that, so I was sent a host of tutorials.

I bollixed up the making of the bias tape yesterday.  But there are a few important things to know about making bias tape — start big. Don’t try to make 1/2″ double fold bias tape the first time; go big, and make 191″ length of 2″ single fold bias tape, so you wind up with 1/2″ double-fold.  It’ll be much easier.

I also discovered that I had a gadget which allows you to feed a strip of tape into it at one end, and folded tape comes out the other, ready for the iron.  I bought it a while ago on the recommendation of someone, and then never used it.  Now I’m using it.

It’s a nice discovery.

This morning I made my first potholder (at least, my first potholder since I was six or eight years old).  Two leftover quilt squares from one project with some leftover batting between them, and a couple of strips of bias tape — one to make the jaunty red loop for hanging it up by the stove, and one for the blue trim around the outside edge of the potholder.  It still needs some trimming and some extra zig-zag stitching to hold it together, but it’ll do for a first effort.

There are worse things to do before breakfast.

Quilts: walking foot

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Ivy at Circle Thrice responded beautifully to my comment with a post about the magic of making things ourselves, and particularly for people that we care about.

It’s not a post I wrote myself, alas.  I shoulda.

Because this blog, for better or worse, is a blog about magic.  In large measure it’s a blog about the power of making things; it’s blog about the power of co-creation — the act of pulling the materials of the world to you, shaping them and changing them according to a particular vision, and producing something on the other end which is more than the sum of its parts.   Something of your self is woven into the finished product, for better or worse.  Yet in many ways, it is better than something bought through anonymous channels, through the mercantile trade of your hours for abstract concepts, and the trade of abstract concepts for the physical goods of your life.

Today I broke down and went to the local fabric store. It has a name that sort of rhymes with pollyanna, but not really.   I’d heard there was this magical tool there, something akin to a wand of fire or a disk of earth — a walking foot.  (I also needed binding for the quilt I’m holding in these pictures. The binding is the pale green band around the outside of the quilt — it’s better to make that by hand from a 100% cotton fabric, but I am not good at making bias tape or binding — I could spend as long making enough bias tape to make this quilt, as I spent making the quilt).

A Walking Foot? I hear you ask.  Don’t most normal feet walk? Not on a sewing machine, they don’t.  A walking foot attaches to the low shank of a sewing machine; and it has a mechanically-driven lever arm that hooks on to the needle’s drive shaft. The result is that the walking foot engages a second pair of dog-legs (those are the feet on the face of a sewing machine, that advance the fabric through the needle’s binding mechanism.

This particular quilt had been giving me trouble. Truthfully, all of my quilts give me trouble in the same way. The first part of the work involves stitching together squares. I’ve gotten a LOT better at that work. The second part involves quilting three layers together — in this case, the topper of green and blue squares; the batting, basically a thick layer of felt; and the backing fabric (the dark blue in the first picture).  The three layers can be seen in the third picture.

Today I broke down after doing the first half dozen straight stitches of this quilt. I needed quilt binding anyway. So I went to the fabric store for binding for this quilt, and got the walking foot.

What a difference the right tool makes! The walking foot guides the fabric sandwich into the needle-space with great diligence and accuracy. It’s a supremely powerful focus for the sewing machine, like a lens focusing a powerful beam of light into a laser — swiftly went the work of sewing the quilting stitches.

I was able to finish the rows of the quilting, and then the columns, with great accuracy. And then the binding around the edges went quite easily as well. Before the Walking Foot, this might have taken me the better part of two days of work with my old sewing machine. With the Walking Foot, a few hours at most.

This is my seventh quilt, I think.  It might be my ninth, but I think it’s probably the seventh. It’s taken me seven quilts to learn how to do this well enough, and effectively enough, that I learned what sort of problems I was having, and was able to do the research necessary to find the solutions.  Every single one of seven quilts, I’ve gotten better at this.  They may not be Etsy quality, but they’re a lot better than they were.  In a short while, they’ll be a lot better than they are now.

All aspects of Making are like this — you have to be an apprentice before you can be a journeyman; and you have to do the journey-man or journey-woman’s work work before you can be a master of a craft.  It doesn’t matter if you’re talking poetry or quilting or fashion design or musicianship or painting or carpentry or engineering or basket-weaving — or even magic and re-enchanting the world: Start somewhere near the beginning. Get Better. Keep Going.  To Walk the Path Of Power, the Work Is On You.

Quilts: finished

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Two quilts finished in three-ish half-days. The top one is the penguins from earlier, the bottom one in pink is the owls quilt.  Both are already spoken for, you can’t buy them.

Really, it’s three quilts but I’m having my doubts about the arrangement of materials for the third quilt. I think I could get the third done if I could get some feedback on whether or not people think it’s a good layout.

Here’s the third quilt. Tentatively, anyway.  I’m worried that the dark blue of the starry swirls doesn’t really match the green or the blue of the top of the quilt; and that the baby-blue trim doesn’t match either.  I suppose I could tie it all together with some thread of the right color… but it still makes me a little nervous.


What do you think? Leave me a comment.

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