Triangle quilt

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This is the second quilt I’ve made that uses triangles. The first such quilt I made, I assembled hexagon shaped “blocks” and then sewed the blocks together. With this quilt, I assembled the triangles into rows, and then sewed the rows together. Something went wrong diring the assembly process though. If you look closely you can see the challenge: partway through, I seemed to run out of triangles. So I added more triangles to the pattern. And I wound up with an extra row. The first photo shows the quilt as planned: the second photo shows the quilt top as assembled. 
So this quilt has an extra or unneeded row. Now I have to decide if I’m going to even the work out by adding another row, or leave the thing unbalanced as it currently is.

Quilt: triangles

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Had you told me at the start of this project what a terrible construction system triangles and hexagons were, I might not have believed you. I admit that. But I hadn’t expected them to be quite so much of a bear to construct as they actually were.

It seems simple enough, really. Cut triangles slightly larger than you want them to be. Clip the corners, or imagine them clipped, and imagine a 1/4″ seam allowance around each piece. As you sew them together, either in rows or in hexagon ‘blocks’, the pattern you’ve chosen begins to emerge. Alternate solid and patterned fabrics for a more elegant design with much more visual interest.  Seems simple, right?

Nobody explained what a bear those corners are in the middle. If you want a really elegant point on your star or on the fan of triangles at the center of your hexagon, that’s about 3x more work than “just sewing triangles together.”

Still, sooner or later you have to do it. It’s not possible to just keep building quilts out of squares forever. Sooner or later, you have to grit your teeth, stomp your feet, and assemble a quilt that uses triangles or hexagons.  You make your templates, slice up your fabric, and get to work sewing.
And things go wrong. You mis-marked a triangular piece. You didn’t mark a piece. You didn’t clip the corner of a triangle. You didn’t clip the correct corner at the right angle of a triangle. You removed too much of a corner. Your chalk wore off the piece of fabric. THere’s a dozen (a million) things that could go wrong. It doesn’t matter. “Build the whole prototype,” says a friend of mine in the engineering business. “That way, you know where the serious mistakes are.” There are a lot of serious mistakes in this quilt top.

Still, there are some successes.  Some of my center corners are pretty spot-on.  Some of my external centers look pretty good, too.  Some portions of this quilt look awesome.  And some percentage of those who see the finished product will never know there were any mistakes at all, once I’m done quilting it within an inch of its life.   The perfect is the enemy of the good, wrote Plato, as the words of Socrates.  And so it seems here, too — the more perfectly I try to make this quilt on the first try ever with this technique, the more likely the quilt will wind up unfinished in a drawer for months out of frustration.

And so it is that the quilt is here — pinned to its batting and backing, and ready for the quilting-sandwich: layers of stitching that will bind the upper layer to the bottom layer through the middle layer.  And then there will be bias tape to make, and edge-binding.

And then it will be done.

It’s certainly not the best quilt that I’ve ever made.  It’s certainly the best triangle-based quilt I’ve ever made, given that it’s the only triangle-based quilt I’ve made (though not the only hexagon-based quilt I’ve made — see English Paper Piecing and some of my further insight.)  But most of what it is, is a learning experience.  I’ve made this quilt, and I now know enough of the process that a range of similar patterns and workings are now open to me.  I can do this again and again, as needed and as desired.

Just don’t ask me to make a triangle-based quilt for free. Ever.

Quilts: cut and sew

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I want to learn the core angles of quilt sewing. Since most quilts are simply tiling patterns writ in fabric, a large percentage of this work is done in squares or rectangles on the one hand; or triangles, diamonds, and hexagons on the other.  These shapes and their variants are pretty much the only ones that tile easily. 

I started by making some six-pointed stars using a flat triangle pattern. When three flat triangles are grouped, one gets an equilateral triangle. when one groups six equilateral triangles, a hexagon results. Half-hexagons can be used to form an edge to a field of hexagons, turning a hexagonal tile patttern into a rectangular ore square field. Many hexagons and half-hexagons together form a quilt… Who knew?? 

Much of the early work consists of lining up sheets of fabric and then putting a template on them to slice out triangles.  I felt like I cut out hundreds if not thousands of triangular fabric tiles yesterday. You can see the piles of them in the first photograph here, a lot of grays and blacks and very dark blues, with some Celtic knot work fabric, too. 
Once that fabric gets sorted by color and type, it begins to feel like not enough, though.  

Nonetheless, one has to keep going. Breaking up big pieces of fabric into smaller ones just results in a mess. Fabric has a warp and weft that holds it together.  Once you start cutting into it, you break up its internal integrity and it will start to unravel.  You’ve dissolved the bonds that hold it together.  Now you need to begin to recombine it.  

The key things to consider about that recombination are color, texture and weave.  People like complementary colors rather than clashing colors.  They like patterns, but they don’t want too many patterns next to one another.  There need to be places where they can rest their eyes on relatively neutral hues, so that a patterned fabric can then grab their attention. That’s a lot to hold together in mental clarity. 

And so we begin with somethiing relatively neutral, and matching the stars in certain particulars.  
Hexagons have a particular logic to them when you start with triangles, as I have. Quite naturally the three stars are going to draw the eye first and foremost.  So the quilt has to be built out around them. I have enough fabric to make twelve or thirteen more of these two-grays hexagons, but not enough to make a whole quilt this way. So my next step is going to be to construct another pleasing hexagon design, and interleaved the two-tone gray hexagons with that new design, while trying not to distract from the stars.  My partner also recommended making more stars but in radically different colors. That could work too. 

Yesterday at the fabric store, I met a woman who was making fabric furnishings for a Russian Orthodox congregation: linens for the altar and stoles and robes for the clergy.  She was working on the stiff linen and brocade chalice cover, and had come in to find some more gold braid for the cover. It was beautiful. I have a long way to go yet, but it was a reminder that all kinds of people need all kinds of custom sewing work. Increasingly I’m prepared to handle it. 

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: finished

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

Eight pages of geometry

​​​The geometry book is finished.

I’ve been working on this project on and off since 2013. It’s a Japanese Album moleskine, sometimes called an accordion-fold book, of about 50 leaves or panels.  At this point, both sides of every sheet of paper in the book are inked with 111 geometry problems in both diagram and text.  (technically, there’s space for about three more on the inside of the front cover).

I began this project when I came to the realization that geometry was part of the underpinnings of good design work — that if you could see the key elements of the geometry underlying a project or a design, that the quality of your work would improve because you understood how different relationships were managed between various parts of the project.  Because ultimately, geometry is about relationships.

More than that, this project has been about self-discipline.  I started the book at one scale, then shifted to a tighter scale after about fifteen panels.  Then I stopped for a good long while, somehow afraid that I’d ‘ruined’ it by the change in scale.  Then, I picked it up again, and worked all the way to the end of one side of the book, and about seven panels into the other side. There was another long pause, maybe as long as a year.  About six weeks ago, I picked the project up again.  I couldn’t find the right marker pens that I’d used to start the book. I shifted to different pens (Prismacolor was the first brand, at 0.5mm; Staedtler triplus fineliners the second, at 0.3mm). I got better results, especially on the more complex constructions, with the new tools.

And this morning, I finished.  I woke up early, and I came downstairs. I finished the page on ellipses that I began yesterday, and then began work on the page on spirals.  The spirals page went far more easily than I expected.  It was simple to turn from that to the final page, which is in part about the Golden Section, and the process of laying out multiple proportions.  I thought that page was going to be difficult, too, but it wasn’t.

And then I was done.

It doesn’t actually feel like it’s done; that may take a little while to sink in. But the project (except for maybe some unusual problem not covered by the earlier work, that can go on the inside front cover), is now complete.

​​More than any other project I’ve done, though, I feel like this is the one that lets me say, “I am an artist and a designer.”

Hello.  My name is Andrew Watt. I’m an artist and a designer.

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

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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.

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