Designs with Lines and Circles, by Paula Beardell Krieg

My workshop in making designs with lines and circles attracted a good number of people last month. I wrote about the first class already, and here’s my wrap-up post, which is a few weeks late, but, hey, it’s summertime and my children are home.

Designs with Lines and Curves class

Designs with Lines and Curves class

The most wonderful and surprising aspect of the class was not only the number but the age range of the participants! In fact, the class attracted ‘tweens through adults, and since this way of working was new to everyone, the group felt cohesive.

Michael's , Six petals

Michael’s , Six petals

At this second class there were a number of people who were coming for the first time, so with them, we started off creating intersecting circles to create the six-petal pattern that I had introduced to the group last time. People colored them in according to their own style.

Six petal pattern

Six petal pattern

I love the range of styles that I saw. Some of the work was bright and bawdy.

Joyce's six pointed star

Joyce’s six pointed star

Some of the pieces were dreamy and meditative.

Karen's Six-Petal image

Karen’s Six-Petal image

Some pieces were cheerful and carefully considered.

Kathy's 12-petal image

Kathy’s 12-petal image

For people who wanted to go just a step beyond the six-petals, I showed them how to transform the six into twelve petals.

Okay, I know that the image above is hard to see, but, actually, that’s the point. This is what I handed out to people who were ready to move on to a more complex  set of shapes. While I worked with the newcomers, I asked the rest of the group to look at this page and start finding shapes that they might like to highlight in their own pieces. That, after all, is one of the coolest things about this way of creating designs: there are an infinite number of individual responses to the same underlying architecture.

Eight Petal design

Something surprising happened. Some people were happy to use the PDF that I handed them, and to color that in. The point of the class (I thought) was to show people how to create the shapes for themselves, but not everyone wanted to do that.

Diane's work

Diane’s work

It’s fascinating to me to see what unexpected things people do in classes. The fact that there was a group that happily and prolifically just colored was fun to see.

Jeanne's Work

Jeanne’s Work

There was also a group who was very interested in learning how to make the underlying designs for themselves.

Michelle's work

Michelle’s work

Wonderful.

I didn’t end up taking many photos during the third class that I taught. It turns out that what I brought in was way challenging, and I spent most of the class focused on helping people be successful. What happened? The first class I showed a six-pointed star (or six-petal) design, the second class I showed an eight-pointed star design, so for the last class it seemed logical to me to show a five-point star design. Making a five-pointed star design turned out to be much more difficult for people.

One of the highlights of the class was showing people a site that turned their work into hyperbolic tiles.

hperbolic tile

Hyperbolic tile

If you don’t know what a hyperbolic tile is, well, it doesn’t matter. Just upload an image into the site  and hit the “generate tiling” tab. Within days of showing this to people, I started see hyperbolic tilings show up in my FB feed.

All told, the three workshops were just wonderful to share with the people in my community.

Here are the links that I found useful for these workshops

Intersecting circles for Seed-of-Life Geometry

Eight Pointed Star Geometry PDF

Dearing Wang’s Youtube channel

Dearing Wang’s HOW 2 Draw Tesseract – Octagram Into Infinity  https://www.youtube.com/watch?v=CqnH1y1HpF8

Golden Ratio Star Pattern

to make a Hyperbolic Tile http://www.malinc.se/m/ImageTiling.php

Pop Ups with more Pop ups

Pop Ups with more Pop ups

In the summertime, when school is not in session, I’m on my own in terms of deciding on what kinds of projects that I want to teach in workshops. Last week I taught for five days  at the local community center.  My sessions with the kids were 40 minutes long, and although I prepared for 30 rising third and fourth graders, there was no telling how many students would attend each day. I had originally thought I would make a plan for the week, but quickly realized that it was more satisfying to create projects each day based on what I found interesting in the children’s work from the day before.

Making Pop-ups in an Accordion Structure

Making Pop-ups in an Accordion Structure

My own goal for the week was to do explorations with shapes and symmetry.  On Day 1 we made a four-page accordion book and did some cut-&-fold to make pop-ups. The students were amazing paper engineers;  With impressive ease, they created inventive structures.

Pop-up Worksop

Pop-up Worksop

There were plenty of counselors in the room, and from this very first project, these counselors joined right in with creating their own projects.

Overlapping Rotated Squares

Overlapping Rotated Squares

I was so impressed with the students’ folding skills that the next day I helped them create an origami pamphlet that contained more pop-ups, as well as some interesting other cut-outs. What turned out to be the most interesting work on Day 2 was how much the kids liked the little bit of rotational symmetry that I encouraged them to do: I gave them each a square of paper, asked them to trace it on to the cover of their book, then rotate it and trace again.

summer squares 3

These students like the shapes created by shapes, so the next day I brought in a collections of shapes and asked them to arrange tracings of these shapes on a piece of heavy weight paper, which was folded in half.

Tracing Shapes to Create  More Shapes

Tracing Shapes to Create
More Shapes

Students seemed to enjoy creating these images.

summer shapes 2

After they created the outlines they added color.

Colored Shapes

Coloured Shapes

When the coloring was done we folded the paper, and attached some pagesto the fold so that the students had a nice book to take home. The kids seemed to like this project and made some lovely books, but I ended up  feeling like there wasn’t anything particularly interesting going on with this project in terms of explorations of building with shapes. So …

Building Stars and Hexagons with Regular Rhombuses

Building Stars and Hexagons with Regular Rhombuses

…the next day I brought in colored papers that were printed with rhombuses, as well as some white paper printed with a hexagon shape. Each student filled in their own hexagon with 12 rhombuses.

Making a Hexagon with a Star in the Middle

Making a Hexagon with a Star in the Middle

My plan for this project was to have each student make their own individual hexagon then put them all together on a wall so that it would be reminiscent of a quilt.

Paper Hexagon Quilt

Paper Hexagon Quilt

Here’s our paper quilt made from 22 hexagons!

The next day, Day 5, was my last day at this program. I liked the engagement with and results of how the students worked with shapes when they were given structure. There’s a balance that I try to honor of providing structure while allowing individual choices. For my last day, then, I decided to give the students a page that I created that is based on the geometry that uses intersecting circles and lines to create patterns.

A work in progress by one of the couselors

A work in progress by one of the counselors

If you look closely at the photo above you’ll see many different lines and curves overlapping and crisscrossing.

summer geometryI asked students to look for shapes that they liked, to use the lines that they wanted to use, and to ignore the lines that they did not want. It was interesting to watch how the students worked; I was particularly interested in seeing how some children chose to start looking at designs starting in the center, while other children gravitated to the outside edges first.

summer geometry 8

Some students filled areas with color, while others were happy to make colorful outlines of shapes.

summer geometry 2Some drawings were big and bold.

summer geometry 5

Some drawings were delicate and detailed.

summer geometry 4I think that every one of the teenage counselors sat and made their own designs, right alongside of the students. Actually, I think that my favorite unexpected outcome of the week was how involved the teenagers got with the projects.

summer geometry3

This last project of the week was my own personal favorite (though the quilt project runs a really close second). I had never done anything quite like this before with students, and was really surprised to see how much they enjoyed this work, and how differently they each interacted with the lines and curves. This kind of surprise is what’s so great about summertime projects.

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