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 Book


Some of the geometry book I'm working on...

Eight pages of geometry

I forget which post Gordon said it in, but at one point he noted that nearly all books prior to the invention of printing were books of magic.  Sure, on the surface they might be called medical textbooks or scientific textbooks or books of geography or mythology or history. But at some level, all these books were books of magic — they were intended to change consciousness at some level.

Rufus Opus said something similar about making lamens. A lamen is usually a disk or a square that you wear on your chest during the conjuration of a spirit.  The act of writing one, of punching a hole in the parchment, and putting it on a string or a chain or a lanyard, is a creative act.  If the emblem you write on the lamen is the signature or symbol of a spirit, your hand is going through a kinesthetic meditation on the nature of the relationship between the conjurer and the spirit.

Something similar is happening as I create this book.  It’s a Moleskine Japanese Album, the larger size, so the pages fold out into this lengthy ‘wall’ or ‘screen’ of emblems — about 5 1/4″ x 8 1/4″ inches per panel, but about 115 1/2″ long — call it about 9′ 7 1/2″.

I think about this project from time to time — more lately, since I’ve been working on it the last few days — and every time I do, I’m somewhat more dismayed at the current state of geometry teaching in the United States.  By all the accounts I’ve found, and by the anecdotal evidence I’ve collected on my own, we’ve stopped teaching students to use rulers and compasses in the study of geometry.  It’s too hard to remember procedures, or students don’t know how to use those flimsy plastic compasses well and the good ones are too expensive, or Euclid isn’t widely available, or … or… or…

The excuses multiply like dandelions after a rainstorm.

I don’t know that this book “will become an heirloom of my house forever,” as one of the somewhat-more-fictional sagas would have it. But I do know that I learned more geometry from the construction of the book than I ever learned in a class.  And I wonder if there’s not a better way to teach geometry embedded in that discovery?

  • Each student gets a good compass, a good ruler, colored pens or pencils, and a blank notebook.
  • Each student learns the construction for a harmonious page layout
  • Each student learns a set of procedures for:
    • Perpendicular bisectors
    • duplication of angles
    • construction of parallel lines
    • construction of similar triangles
    • construction of polygons from given sides
    • construction of polygons within circles
    • transference of a given length or distance to another angle
    • construction of nets for 3-dimensional solids
    • construction of the root-2, root-3, root-4, and root-5 (phi/Φ) proportions
    • division of lines into thirds, fourths, fifths, eighths, ninths, and sixteenths
    • construction of grid and tile patterns
    • construction of simple polygonal combinations to find the sides of super-polygons.

This benefits future craftspeople, because they’re receiving an education in proportions and common mathematical relationships, and it’s not all algebraic notation.  It brings back the beauty of geometry to the mathematics classroom.  It gives all of society a common language for seeing mathematics in the natural world.  It trains future architects and engineers in precision diagramming, and gives future laypeople practice in reading such diagrams.

And it creates hundreds of unique copies of books of practical geometry that are themselves handbooks to a forgotten magic — a magic of beauty, of proportion, of color, of relationship, of graphic design. Students would get to learn ALL of that in the process of producing their own books over the course of a semester or a year. The quality of their book would gradually improve, as their understanding of the geometry improved, and as their love and care of the book improved. Think of all the other studies that could be folded into the creation of the book, too: handwriting, color theory, graphic design, book design, clear writing about mathematics, methodology.  The book is a grade — and students who kept their book up to date would find it useful while taking tests to remember what they had created in their own handwriting. The book itself would be a palace of memory for all the geometry they had learned, just as mine is.

All of the actual constructions are covered in Andrew Sutton’s book Ruler and Compass.  But actually implementing it is on the individual teacher.  And it’s likely the case that the teacher will need some substantial support from an administration that sees and cares about quality instruction.

But it can be done.

Fidgeting and Hand Skill

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There’s a lot of outrage about fidget spinners right now. Some teachers are saying ban them! Other teachers are saying, Let students have them.

It’s a stupid argument.

Remember yo-yo’s? Finger skateboards? gear-powered spinning tops? String powered spinning tops? How about Rubik’s Cubes which made a comeback a couple of years back? Wind-up cars that did tricks?

Fidget Spinners have a place and a time in children’s hands.  And as some of you know, one of my mantras or principles is that What the Hands Do, the Mind Knows.  But here’s the thing.  If you don’t want the latest finger-toy-de-jour in your classroom, then you have to find other ways to put those hands to work, learning actual hand skills:

  • teach calligraphy
  • teach knitting
  • teach drawing
  • teach geometry with an actual ruler and compass
  • teach the use of a slide rule or abacus
  • teach the building of automata (cogs and gears)
  • teach carpentry and build yo-yos, finger skateboards, spinning tops, and fidget spinners.
  • teach contact juggling
  • teach juggling
  • teach beading
  • teach woodcarving
  • teach origami
  • teach flint-knapping
  • teach ceramics throwing on a wheel
  • teach students 3D geometry through the assembly of nets of the Platonic solids.
  • teach color theory and coloring at a more advanced level through color pencils.

The fidget spinner is an outward and visible sign of an inward need — a need for the hands to learn something.  Kids’ hands fidget because they’re of an age to want to do something, not just sit still.

(And I KNOW that we’re not making them sit still in schools — that they’re doing personal practice as well as listening, reading, writing, reflecting on their work and all that sort of stuff. That’s not what this is about).

Human beings need to use their hands. We learn things through manual dexterity, through touch, through manipulation of objects.  Our constant rejection of the toys-de-jour, be they yo-yos or balsa wood flyers or paper airplanes or fidget toys is part of the reason kids don’t learn as much in school as they could.

So if you want to fidget-spinner proof your classroom… figure out WHAT tool or hand-skill you want your students to have, learn HOW to teach it, and then TEACH THAT.

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?

Wood: trestles

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On Sunday I borrowed a friend’s woodworking shop to produce a couple of trestles for a table. They sort of look like sawhorses, but they’re not. They’re intended for lighter duty than that. I still have to produce the top of the table, which will have two bars or cleats on the bottom to help lock the table and the trestle together.

These are based on a medieval design produced by the St. Thomas Guild, a medieval reconstruction group in the Netherlands. They are pretty modern, though. I’m trying to decide if I want to add in the fancy carving and tracery work to them. I know how to do that work, I just don’t know if it will be worth it in DIY shop pine.

Some things to think about —

  • Adding a second board across the bottom for stability would help these trestles be less wobbly.
  • Adding a wedged mortise to the top cross-board would also make them less wobbly
  • Adding a cut-out to make the triangles more like a pair of legs would add stability, as well.
  • The table-top will have to have two cleats or bars on them, to slot into spaces at the top of each trestle.
  • Adding some pegs to the bottom of the table top; or to the top board, that slot into the table top, would also improve stability, generally.

There’s a lot of things to think about.

In general, though, I like this idea.  The trestle table has some serious advantages for me, in that I can take the table up or down as needed, and have the flat surface or not as I need.

Additionally, in reviewing the St. Thomas Guild website, I see that I can design this table top to do many things that may help it be quite portable or adjustable.

Table Top DesignMy initial thinking resembles something like this — a kind of construction known as “frame and panel” (which I’d like to learn), with four types of members:

  1. Dark green outer frames, with one groove and three mortises.
  2. Internal ribs, with a tenon on each end and a groove on each side (purple)
  3. four panels (mottled blue) with a tongue carved all the way around them.
  4. Two internal frames, with three slots and a groove (light green)
  5. Four outer frames (yellow) with tenons on each end and a groove on one side.

The blue panels thus fit into the groove on each side.  A quartet of hinges join the two inner frames to one another, so the table can fold flat and store more easily;  or be arranged to provide a wide or narrow table as needed.

I may have to rebuild the trestles to accommodate the larger table surface. But my understanding is that panel and frame construction is fairly lightweight, and this might do quite well for my general needs.

Dimensions of the surface still need to be worked out.


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.

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