# Wind River Beauty, Math Part 1

In 2017 Jim and I drove thousands of miles in a number of different trips. When you’re in the car together that much, literally a few inches apart, it helps to have entertainment. Fortunately, we like to talk with one another, so the types of things one might muse about silently instead become topics for conversation. For example, after noticing a stop sign and considering how it looks like a snowball block, I asked, “If you start with a square and want to make a regular octagon from it, how do you calculate the length so each of the 8 sides is the same?” Huh?

Okay, look at the two illustrations below. The one on the left is a stop sign. It’s a regular octagon, meaning that all of the angles are equal and all of the lengths are equal. The diagonal segments of the octagon are the same lengths as the horizontal and vertical segments. I noted the dimensions as a for the vertical and horizontal segments, and c for the diagonal segments. As you can see, a = c. (Click the image to open the gallery and see larger.) The segment lengths are all the same. The dotted segment noted as b is not part of the octagon. If you extend the vertical and horizontal lines to create a square, b is the extension.

On the right is an illustration of a square, red & white snowball block. (This specific snowball block is designed to pair with something like a 9-patch block.) For the octagon (white, 8-sided shape,) the angles are all the same. However, the lengths of the octagon line segments are not the same. The diagonal segments of the octagon c are longer than the horizontal and vertical segments a. Why? For this particular block, each side of the square is cut in thirds; a = b. Going down the left side of the square, the top red segment b is equal in length to the center white segment a, which is equal to the lower red segment. The equal lengths make it easy to pair this block with a 9-patch. But the equal lengths of a and b mean the diagonals c are longer by a factor of 1.414. The general idea is the same for all snowball blocks, with the length of c the diagonal dependent on the length of the two triangle legs. See the primer on the Pythagorean theorem at the bottom of the post if you want to know more.

So how do you take a square and make a regular octagon from it? I’m not bad at math but will be the first to admit I didn’t learn my geometry. Jim worked it out for me. What he found is

b = .707a
2b = 1.414a
==> side of the square = 2b + a = 2.414a

Why does it matter? At the time it was just curiosity, but I quickly found a project to apply it. In spring of 2018 I took a workshop with Toby Lischko on making New York Beauty blocks. She taught a simple way to use curved rulers and paper piecing to create these lovely, complex blocks. This was mine.

After I made it, I thought about how to use it to center a quilt. My design idea would work best if the center was a regular octagon.

With Jim’s formula in hand, knowing the size of the square, I solved for a and b, which let me know how big to cut the stitch-and-flip squares to make the corners.

I wanted a center block finishing at 17″. (Why 17″? That comes later, more math!) That means
side of the square = 2b + a = 2.414a
17 = 2.414a
a = 17/2.414 (just dividing both sides by the same number to solve for a)
a = 7.04, or just barely over 7″.

Since the finished side of the square is 17″ and a (the center segment) is 7″, the other two segments b are 5″ each. I cut my stitch and flip corners 5.5″ each. This is the result. The finished length of the diagonals (along the purple/orange seam) is the same as the finished length of the orange segment along the horizontal and vertical sides of the square.

#### Pythagorean Theorem

Here’s the concept. The picture below shows a triangle that is 1″ on the vertical and horizontal sides. The diagonal measures 1.414″, which is the square root of 2″. (Check with your calculator if you don’t believe me.)

For a right triangle, the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the other two sides. We often see this expressed as a² + b² = c². To find c, take the square root of c².

In the case to the left, a = 1; a² = 1; b = 1; b² = 1; a² + b² = c² = 2; c is the square root of 2, or 1.414.

In fact, the diagonal of every square is 1.414 times the length of the side. So
length x 1.414 = diagonal.

1″ x 1.414 = 1.414″
2″ x 1.414 = 2.828″ or close to 2 7/8″
3″ x 1.414 = 4.242″ or close to 4 1/4″
4″ x 1.414 = 5.656″ or close to 5 5/8″
and so on.

That also means that if I know the diagonal of a square, I can find the length using
diagonal/1.414 = length. For example
6″/1.414 = 4.243″, or very close to 4 1/4″.
This is also useful in the next step of the Wind River Beauty.

Agreed, you gotta be something of a math nerd to work through all this. I’m glad all my quilts don’t require this process, but it’s a wonderful tool to use for a few.

# Class Projects in 2018

My guild has had some terrific workshops in the last few years. In 2018, I participated in three of them and added to my tool kit of skills. I share a bit about them below, in the order I took them.

Kim Lapacek of Persimon Dreams
Kim Lapacek brings a joy and enthusiasm to her work, and her workshop, that I’ve rarely experienced.

Kim led a workshop in the style of her Project Quilting challenges. Nine guild members spent the day inspired by her take-no-prisoners style of quilt-making. She goes ALL OUT, with techniques, embellishments, color, and pattern. As our challenge, she provided fat-quarters of base fabric as well as two more fabric pieces to each of us. We were to create and FINISH a quilt top in the six-hour time slot, using those two printed fabrics and NO straight-edge ruler. In addition, we were given a limit on how much fabric we could bring — only the amount that fits in a brown paper lunch sack. Also the fabric pieces we brought were supposed to be scraps, less than a fat quarter. While that lays a lot of constraints down, the subject or direction of our individual projects was completely up to each of us.

Influenced partly by her own “amazing technicolor dream heart quilt” and partly by a project I’d been wanting to make, I decided to use a rainbow color scheme to recognize LGBTQ rights as basic human and civil rights. It might be a poor shorthand, but it is eye-catching.

The verbal message is plain in black letters.

This project is like nothing I ever did before. It hangs behind my ironing station, and every time I stand there, it buoys me a bit.

Cathy Geier
Cathy Geier is an art quilter focused on landscapes. Her style would probably be called “collage appliqué,” though she incorporates piecing, especially into the backgrounds. She’s also quite fond of amending her fabrics with paint and markers, allowing some subtleties not available from the fabric alone.

In our workshop with her, we learned some basics of creating a landscape quilt of a forest scene. With commercially-available fabric, we cut tree trunks and glued them to a base background fabric. Diluted white craft paint helped turn the birch trees a paler grey, and silver Sharpie markers applied to one side of the trunks gave a sense of dimension. Flowers and shrubs came next, and then leaves. Leaves were mostly adhered using a fusible web rather than glue, but either would do.

At home I added a border and did the quilting. This was my first “collage” quilt and I’m very happy with the result, and with what I learned. The part that makes me less happy (and I know this wouldn’t bother many people) is that it doesn’t feel like my quilt. I can’t display it because I didn’t design it, and likewise it’s hard to give as a gift. Maybe that’s just weird of me to feel this way… But maybe because of that, I like the back that shows the quilting as much as the front.

The gallery below shows a squared-off photo. Click either image to see bigger and with right proportions.

Toby Lischko
Toby Lischko specializes in using mirrors to create fabric design symmetry, and in curved piecing, especially in New York Beauty blocks. My guild was treated to the first topic for an evening presentation, and to the second topic in Toby’s workshop.

Using her method and rulers, curved piecing was a snap. I honestly was surprised at how easily and well my blocks turned out. In class I made two quarter-circles; at home I made the other two and set them in a background of orange Grunge.

I added corners in purple and designed the Lone Star-style star point. I need to take the star point apart and rebuild it so my seam allowances and sizing are better. This is a low-priority project so will carry into next year.

I am very fortunate to have opportunities like this. My guild has some great things planned for the coming few months, too, and I look forward to them, too.

# Mess

Sometimes it’s hard to know where to start. I have lists of things done and lists of things doing and lists of things to do! I have a mess in my studio, the product of having several projects going at the same time. What should I do first? What should I write about first? Perhaps the first quilt I finished this year! Perhaps the one I’m working on right now! Perhaps the one I’ll take up on Monday!

So confusing… But in the interests of some forward movement, I’ll show you some pix of my studio late yesterday.

Now I know, this is not most people’s idea of a mess, but it is for me. That’s one of the reasons I tend to be very linear in my making, with only one or two active projects at a time. I can finish something, CLEAN, and move on to the next thing. With lots of active projects I can’t put things away.

Here is my list, not in priority order:

And here is my “current” project.

I started the center block on Tuesday in a workshop with Toby Lischko. It is a classic New York Beauty, a challenging block to make. But her instruction, tools, and technique made it very easy. I modified the size of the outer background (Moda Grunge in orange) to make it 17″ finish instead of 16″. (Math stuff — I won’t go into the details now but it should set up all the rest of the sizing well.) And I added corners in purple (more math stuff for how I decided the size. Details later.) And I designed the Lone Star-style star point. I need to take it apart and rebuild it so my seam allowances are better, but later I’ll be glad I took the time to do that.

HOWEVER now it’s time to switch gears, so this project, called “Wind River,” will just wait for a few weeks. Instead I have a secret project to do as a wedding present for Son and his bride. Since they get married four weeks from today (HOORAY!!!) I have to get in high gear on that. (And oh yeah, I better make my purse, too!) This is my linearity kicking in. Later I can be messy again. 🙂