Thirty Days of Making: Geometry Text page

I’m in Day 18 of a short series: Thirty Days of Making. Every day for the next thirty days, I intend to make something, anything, that is in some way connected to school. There won’t always be pictures, and I reserve the right to credit myself for things that I help my kids make. But I’ve decided that I need thirty days of maker success and maker failure under my belt to be a better designer.

I’ve decided that artwork counts, but not writing (unless it’s part of the art, like calligraphy). Digital work counts, but it has to be useful or publishable.

Some days there will be pictures, some days there won’t be. Each blog entry will contain a list of some of the materials and tools, a quick review of the success or failure of the Making, and a reflection on what I think I learned from the endeavor.  (My friend Alicia is beginning a new series along these lines, 12 weeks of the Artist’s Way — I wish her well in her process, go check her out!).

Reason for the Project:

Mostly, I’m stalled.  We all tend to move in ruts, of course, or at least in regular pathways even if they aren’t ruts.  I hadn’t worked on this project in a good long while (not like I don’t have enough other projects going, really), and it was time to put in a good forty minutes or so into the project.

Thirty Days of Making: geometry textbook page Process and Result:

The first part of the work, of course, is to put down the geometry proof that is supposed to go on this page.  Without that step, it’s hard to get anything else done.  So I did that.  This pair of pages is supposed to deal with angles and with similar triangles.

The proof in the upper left hand corner is the proof for drawing in a parallel line with an angled line connecting them; the angled line is to be similar (that is to say, at the same angle), as a given angle in another construction.  Fussy stuff, and that took a while.  In the course of that, I realized that I wanted to put a second proof on the bottom of the page, for the construction of a triangle given a base and an altitude;  but unfortunately I wasn’t able to make the proof come out correctly.  So I have to spend some time with that particular proof, doing it over and over, until I’m sure I understand how it works.  It’s not a particularly complex proof, but I was screwing it up in the manuscript.  And given that every time I put the point of the compass down on this paper, I risk puncturing a serious hole, or ripping the paper, I’d like to avoid learning to do the geometrical proofs incorrectly over and over again on this paper. Really, that’s asking for much trouble in the long run.Thirty Days of Making: geometry textbook page

The next step was to lay down the indicators along both pages for the lines of text.  There are two guidelines for each line of text — the top of the line, which the capital letters touch; and the baseline, which is used as the bottom guide for every letter. Between them is about a millimeter of space, which is the line-spacing for the lines of text.

I do this with a ruler or a t-square marked in centimeters and millimeters, and it’s a tough process, but also pretty meditative; I got into a bit too much of a groove, actually, and drew out more lines than I intended to.  When I go to add in the second proof on this page, I’m actually going to have to erase some of the lines.

Every line has to be marked, or it’s really easy to screw up the spacing of the text as I pencil it in later.  No easy task.  But there’s also this interesting task of flowing the text lines around the diagram of the geometrical proof.  You don’t really want the lines to overlap; and you actually want the geometric proof to be offset a bit from the lines, so the text doesn’t completely overlap with the key lines in the diagram.Thirty Days of Making: geometry textbook page At least, that’s what it feels like it should be for my work, or at least for this work.

The overall results of the work are a page of lines for a single geometric proof that is, frankly, just not important enough to warrant this much discussion of it.  I mean, if it had some deep ritual significance, maybe I’d devote this much space to it, but I can’t think of anything to write about drawing similar angles that would require this much physical space.

Thirty Days of Making: geometry textbook page Accordingly, I am going to have to erase some of the lines in the lower half of the page (probably on the lower-right), and pencil in another geometric proof.  I’m thinking of doing the problem about the altitude and base of a given triangle, and then adding in the alternate lines.  It’s just that the problems detailing how to find two sides of a triangle from a given side and angle are all rather finicky to draw correctly, while being easy to intuit.  So, I’m not looking forward to the practice of these actions, and I want to put it off.

And now it becomes clear to me why I have been delaying on this particular project for so long.

Reflections on my Learning

Well, for one, it’s clear why we give students lined paper now, rather than making them create their own. Even with a ruler, it’s an annoyance.  Doing it solely by geometry would have been even more labor intensive than this was, and this was pretty time-consuming.  Somebody might ask “why go to this trouble?” And the answer is, “it is beautiful, and it’s powerful, and it’s deep learning.

But it’s MY deep learning, not my students’ deep learning.  I showed this art textbook to our school’s two geometry students, and they were deeply intrigued, and wanted to lay out a few pages of their own… but they don’t want to lay out a whole book this way.  I don’t think they do, anyway.

I’m not sure I do, either.  I’ve done fourteen pages now, out of a book of 49 pages – thirty-five to go? Really?  Each page is a very deliberate work of art; and the whole thing is going to be a very portable and beautiful work of art. But it’s also going to be painstakingly difficult to complete at only a page or two a month. I understand medieval scribes much more clearly now.

Reflections on General Learning

I was greatly slowed down in this project by stopping to consider photographs.  I took more than I thought I could use, and took them at various points during the process; I was also experimenting with geometry proofs along the way, both in the book and on separate sheets of paper, and I found I was getting frustrated.

Today, in Maker Lab, a lot of my kids were giving up on our project of making gauntlets for Halloween costumes. Many of the kids in the class are of an age where they would rather dream than work — they’ were excited about dreaming up the core ideas of the gauntlets, and the electronics inside them. But they’re now in the challenging part of the work where it doesn’t actually function without some physical labor and some mental inputs, and most of them shied away from that at the last minute.

Rather like me in relationship to today’s project.

Which strongly suggests that the dreamer problem is not actually limited to children of a certain age. It’s rooted in who we are, perhaps as a culture, perhaps as a species.  Hard work is complicated — careful cuts with knives and paper patterns, fussing about with paper patterns, ruining parts of the work with too much glue from a glue gun, assembling a set of cut parts only to discover that the glove is too big, or too small… Difficult.  Dreaming is easier. But, as a parent said to me today, “If you don’t paint the boots from Goodwill silver the weekend before Halloween, you don’t get to be a silver robot on Halloween.” A certain amount of work ahead of time is necessary for results in the physical realm to appear.


Three of five stars.  Progress on the project, but no genuine completion.  Learned a few things, but mostly working in a mode and methodology I’ve already worked out.  Learned that I need to put in more effort learning these specific geometrical proofs a little bit more clearly.

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