Accordion Books · geometry and paper

Niche in the Abyss

 “…when you gaze long into the abyss. The abyss gazes also into you.”

― Friedrich W. Nietzsche

Postcard from the edge

I hope you are all doing ok.

I’m doing ok. Beginning to feel less disoriented during these days of pandemic social isolation. I’ve been working at feeling ok. Been following the advice in my last post.

When I can’t make art I clean. When I can’t clean, I sleep. When I can’t sleep I walk around our yard or contact people. The bad days are when I stare into the abyss. Staring into the abyss means watching too much news, making too many trips to the pantry, not getting out of my chair, scrolling endlessly.

I started out drawing and playing around with making accordion books. Most of what I tried didn’t work out.  It felt just fine when things didn’t work out. The only thing that mattered was that I was trying things out.

The little book in the video below I made a couple of months ago, but just recently realized it had some cool hidden moves.

I tried out a bunch of accordion books. Mostly they weren’t interesting or functional.  Below is the the closest I got to finding something I liked, I pretty much stopped with the accordions after this one.

Lucky for me, there are wonderful things that people are posting on-line.

Dave Richeson wrote about how to make a real projective plane (Boy’s surface) out of paper.  Even though I’m mostly clueless about what that even means I do understand the part about making something out of paper. Dave made a wonderful template. I can’t resist a wonderful template. Dave’s design is quite unusual, brilliantly conceived, and just challenging enough to capture and hold my attention.

The only change I made to Dave’s design is that I created attachments using tabs instead of tape. I was delighted that he liked the tabs enough to make one like it for himself.

What was so compelling about making this shape was that I didn’t understand it at all, and I couldn’t visualize how Dave’s template would create what he said it would create.

In fact, this structure was the first thing that really captured my attention during these past few weeks. Slowly I began to remember that what motivates me more than anything else is curiosity. How did I forget that? It really helps to remember that.

I’ve also been working on some Islamic Geometry forms. I saw this tutorial by Samira Mian that seemed so lovely that I wanted to try it out. I actually made it three times. The first one I colored in with pencil only, no color. The second one had rather muted colors.

The next one I did over Easter weekend. Was thinking of spring colors and coloring Easter eggs with my children when they were young.

Then, on Easter Day  Daniel Mentrard posted an exquisite group of amazing geometrically designed Easter eggs, I was inspired to make a few of my own in Illustrator.

I hadn’t meant to spend time at the computer doing these on Easter Day, but it turned out making me feel really happy. Reminded me of how much I like messing around in Illustrator. How did I forget this.

I even mapped my drawing on to a egg shape.

So, it’s happening..The world feels different. I’m not sure what things are going to look like going as this wildcard virus is hovering around us. Still, I’m slowly beginning to feel like I’m finding a niche in the abyss.

Wishing you the best.


Exploring the Language of Patterns

translation design pattern

News Flash: A Codified Language Exists to Describe Patterns. I’ve been so excited to discover the way to speak about patterns.

I’ve been teaching decorative techniques for a long time now. I’ve started trying to use more precise terminology in my teaching, and I suspected there was more to know. I started out looking at artistic and graphic design sites, really I did. I  looked on, I looked on youtube,  and poked around the internet in general. Then Maria Droujkova  pointed me in the direction of something called Wallpaper Groups, and guess what, I landed on sites that described pattern making with precision, using the language of mathematics.

The more I learn the more I understand that what math does is enhance the way that people can describe what’s in the world. It appears that hundreds of years ago mathematicians figured out how to understand and talk about patterns.

Example of Pattern Rotation

This summer I’ll be teaching a week’s worth of classes to young children at our community center. I enjoy showing students decorative techniques, so my immediate interest has been to develop a modest curriculum that focuses on making books that are embellished with style. Even though many of the students will be at an age where they are still struggling with concepts such as “next to” and “underneath”  I hope to introduce them to ways of thinking about concepts of transformation.

Strip Symmetry  is where I landed when I was surfing for a way to find words to describe the kind decorations I’ve been thinking about.  In other words, the patterns I am looking to teach will have a linear quality in the way that they occupy a space, as opposed to being like a central starburst, or an all-over wallpaper pattern. It turns out that there are only a handful of words that are used to describe every single repeating linear pattern ever made.

Translation repeat pattern

 A Translation takes a motif and repeats it exactly.

Example of Vertical Reflection
Vertical Reflection

Vertical Refection mirrors a motif across an imaginary vertical line. The name of this particular transformation confused me at first, as the design itself extends in a horizontal direction, but once I prioritized the idea of the vertical mirror, it made more sense.

Example of Glide Pattern

Glide Reflection can be described as sliding then flipping the motif,, but that description sounds confusing to me. Instead, understand glide reflection by looking at the pattern we make with our feet when we walk; Our feet are mirror images of each other, and they land in an alternating pattern on the ground. Imagine footsteps on top of  each of the paper turtles you might better be able to isolate the glide refection symmetry.

Example of Horizontal Reflection
Horizontal Reflection

Horizontal Reflection mirrors the design across an imaginary horizontal line.

Example of Translation Pattern

Here’s a translation that shifts horizontally, but there’s no such thing as a strip symmetry that translates top to bottom. Instead, convention dictates that the viewer turns the pattern so that it moves from left to right.


Rotation rotates a design around an equator.  The pattern above, as well as the first image of this post, I had considered these both to be rotatation( ( I imagined the equator drawn across the middle of the page), especially if it’s 7 year-olds that I am talking to, but close inspection reveals more. To highlight that I am presenting these concepts with  broad strokes, here is what Professor Darrah Chavey wrote about the image above (the one with the leaves) when I asked for his input:

“As to this particular pattern, there’s a slight problem in viewing these leaves as a strip pattern. The leaves you show are made from a common template, but that template isn’t quite symmetric, and the way the leaves are repeated across the top isn’t quite regular. For example, the stem of the maple leaf in the top row, #1, leans a little to the left, and has a bigger bulge on the left. If we view this as a significant variation, then the maple leaves on the top row go: Left, Right, Left, Left, Right, Right, which isn’t a regular pattern, i.e. it doesn’t have a translation. On the other hand, if we view those differences as being too small to worry about, then the leaves themselves have a vertical reflection, successive pairs of leaves have vertical reflections between them, and the strip pattern on the top is of type pm11. The bottom strip is a rotation of the top strip, but if we view those differences as significant, then it still isn’t a strip pattern (it would be a central symmetry of type D1), and if we view those differences as insignificant, then it would be a pattern of type pmm2, since it would have both vertical reflections, and rotations (and consequently also have horizontal reflections).”
I was excited to get this response to the leaves image, as it reminded me that my newly acquired understanding of symmetries, though useful, is simply just emerging.

So that’s it:

  • Translation
  • Reflection (horizontal or vertical)
  • Rotation
  • Glide Reflection

Darrah Chavey, who is a  professor at Beloit college, turned out to be the hero in this journey of mine, for having made and posted videos on youtube. Here’s a link to one of his many lectures on patterns: Ethnomathematics Lecture 3: Strip Symmetries

Now here’s some nuts-&-bolts of what I’ve learned from making the samples that I’ve posted here:

  • the book I made was too small (only 5.5″ high) because the cut papers then had to be too small to handle easily.  I’m thinking that any book I make with students needs each page to be at least 8.5″ tall.
  • It was easier to create harmonious looking patterns when I started out with domino rectangles (rectangles that have a 2:1 height to width ratio), then cut them in half and half again to make squares, tilted squares,triangles and rectangles.
  • I like the look of alternating plain paper and cubed paper. Folding paper that has cubes printed on just one side accomplishes this.

I am going to enjoy teaching these college level concepts to young elementary children.

Making books with elementary students · Non-adhesive Book · simple book binding

Immigration Journal for 5th Graders

This is the second year I have done this journal project with fifth graders in Saratoga Springs. I wrote about it last year, but in less detail than I plan to write about it today.

This workshop day was requested by the school’s reading specialist, who had done a similar project on her own with a few students.  She was impressed by the students’ reaction to their journals, and thus requested that I come for a day and make these books with the whole grade level, about 70 students.

Books standing on the windowsill

We used paper from large wallpaper sample books. These books are 17″ tall, and about 12″ wide, though the width of the pages is bound tightly with industrial size staples. I cut the papers out of the books, so the final size is 17″ x 11 1/4;, though standard 17″ x 11″ paper would work well too.  Wallpaper books are fun to use because each student’s book is visually unique.

Directions for Pocketed Book Cover by Paula Krieg

The students folded the covers according to the directions above, with one exception. Before the last step of closing the cover, I asked them to snip off the tip of the triangle, about the width of a pencil.

Master Page for Printing Journal Lines on Paper

Students then folded 5 sheets of standard sized paper, 8 1/2″ x 11″, however, to give the pages an antique-like look, we used Ivory faux parchment paper, made by Southworth. The four inside pages were run through the copy machine to copy on the lines pictured above. The outside page is unlined because, well, I like the look of unlined paper when the book is first opened.

Last year, to attach the pages to the cover, we had used a lovely cord called Rattail, from a beading shop, which turned out to be too smooth and slippery: the students’ knots kept coming undone. Yarn, twine or cotton cord could be other choices. Just nothing too stiff, too thick, or too smooth. This year we used 30 inch lengths of  black and silver craft cord to attach the pages to the spine of the book cover, doing a no-needle method of sewing, illustrated in the direction sheet below.

No-needle modified pamphlet stitch
No-needle modified pamphlet stitch

This pretty much finished up the project. I like a book that feels more substantial, so, for a finishing touch, I handed each student two sheets of stiff oaktag type papers to slip into the front and back inside pockets.

Inside pocket

I recommended that the students choose for themselves whether or not they wanted to put a dab of glue on the stiff paper so that it would, or would not, permanently affixed to the pocket. Also, they made their own decision as to whether or not they wanted to add a bit of glue to the edge of the pocket, thus closing off, or not closing off, the possibility of things sliding out the foredge side of the pocket.

I had asked the school to allot 75 minutes per class to make this book. The students were positive, capable, and engaged in their work. Each class finished with 5 to 7 minutes to spare, and there was no rushing. Bsides having such fine groups of students to work with (kudos to their teachers!) another factor that streamlined this project was that students picked out their covers prior to my visit in the class. I will be visiting this school again, seeing other classes. I look forward to taking a peek into the 5th grade again, to see how the students develop these journals.

Binding Loose Papers · How-to · Making Books with children

How to make a Pipe Cleaner Bound Notebook/Scrapbook

Creating a binding for single sheets of notebook paper elevates groups of papers into something more precious.  I’ve recently written some posts on my current favorite way of binding loose papers. The printable hand-out above goes into detail with the steps of  using a pipe-cleaner binding to make a handsome folder.  When I made this with Indian Lake students we used colored papers for the covers; when the students I worked with in Saratoga Springs made it, we used black covers. Either way,  they looked great.

Click on the image on the left for a black & white version of the above hand-out.

Pipe-Cleaner Bound Notebook by Paula Krieg
Pipe-Cleaner Bound Notebook

The students have been filling these folder with their collections of pictures and facts. Good, solid, serious stuff. Personally, I have been enjoying just decorating them.