Geometric Drawings

Ta- Dah!

First Star
Gathered parts of a Star, by Alan, Anne, Bevin Ed, Edmund, Candy, Kianan, Cynthia, Daria, Karen, Stephanie, Mia, Hutch, John G., Ysabela, Janet, Rachel, Susan Joy, Robin, Siri, Simon, Laurie C, , Laurie F, Rowan Jai, Terri and Liza

I have two complete and exquisite images  to show you this evening, the culmination of the efforts of 57 people who filled in a piece of a 12-fold geometric star. The people who gave me these pieces did so  in response to seeing my post Invitation to my Sandbox or from a direct request from me.

Second star
Gatherings of a Star #2 by Kyra, Kimerer, Leif, Daria, Hutch, Siri, Helen, Esther, Cynthia, Kira, Dan, Beth, Kai, Molly, Bill, Carrie, Susan B., Susan Joy, Susan M,, Angela, Susan N., Kathy, Jenn, John G., Kate, Becky, Chuck,,Siri,Ed, Jade, Joyce ,Beth, and Cynthia.

I am over-the-moon happy with the look of these pieces. I had no idea, when I put out my request to people to participate, how this would turn out. I tried to court interest in this project across of wide range of people, and wondered how it would look when they all came together. There are people from age 5 to, well, much much older. We have a  nursery school teacher, elementary and higher level math teachers, a storyteller, a musician, artists, a Phd candidate,  high school students, college students, a geologist, a massage therapist, a writer, bloggers, and people who I don’t know anything about at all.

I had thought to write a long post this evening about many of the stories that come with this project, but it’s getting late and I need to put this project to bed for now. But there two wonderful moments I want to include here.

First, I want to point out tile # 11 in both stars. Here they are:

Tile 11 by Daria and Liza
Tile 11 by Daria and Liza

It wasn’t until the large images were done that I saw that these pieces looked like they had been done by the same person. Not so!  Artist Daria Wilber worked on hers in Colorado while watching the Super Bowl with her husband, and Liza Goldberg, who I believe is a math teacher, and is mother to young children, did hers in hers at school during a prep period. It’s stunning to me how unlike they are to any of the other pieces, and how alike they are to each other.

Here’s another one of my favorite moments:

Tiles #27 and #28 by John G. and Jocelyn

Here are two tiles that couldn’t be more different. John’s is done by computer and Jocelyn’s a highly detailed hand drawing. But look how well they go together! Her red blends into his, and blue lines reach right into her drawing lines. Just exquisite.

I wish you could see this up close like I have been doing, as the relationships and the surprises are so inviting. These were hard to work on at times because all I want to do it look at them.

Putting these together is a reflection of my wanting to lean on the power of art to support the idea that coming together as individuals we create something different than what we can create alone. and what we can create together is wonderful. These stars are my gift, our gift, to an embrace of diversity and unity. Over the next couple of months I plan that some of my posts will include a closer look at some of the stories and more of the images that are part of this piece.

For my friends that think about math, I will be writing something soon on my Google Plus site that will be asking, okay, it’s art, but is it math? (The link will show up here when it’s available.) Also, to anyone who is going to TMC16, I will be coming, and bringing tiles to color in so we can make one of these during our summer camp days!

Thank you so much to all who contributed to this project.

Geometric Drawings

More Designs with Curves and Lines

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.

eight-pointed-star-geometry PDF

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


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

Golden Ratio Star Pattern

to make a Hyperbolic Tile