Yes, awesome, inspiring feelings of awe; magnificent, amazing, stunning. Math rocks!

I truly enjoyed creating Untied, with its free-form, no math construction. Though I used a ruler for parts of it, it wasn’t because the outcome depended on the measurement. Instead, at those instances I was only interested in straight, and sometimes parallel, lines.

However, I love the challenge of a technically difficult quilt, too. For a change of pace, I began a brand new project. The inspiration for it is a piece of fabric I bought several years ago. It’s a fussy historical print that I’ve always loved. However, it’s fussy and historical, and the colors are just off, all of which have made it hard to use. If it is cut into small patches, the impact of the print disappears, but large pieces would require designing just for it. So I am.

I started by pulling from stash, which is how almost all my quilts begin. I pulled all the blues that could work with that print, which meant they had to have a tinge of green and a little grey. It’s the color I learned as French blue. As it turns out, I don’t have a lot of blue with that, and all of it is in scraps or small pieces, other than the inspiration print. We’ll see how far I get before needing to buy something.

Burgundy reds, creams, browns, and cheddar oranges also came out of stash, including from my scrap drawer. I’m trying to commit to using my scraps more effectively. They come in handy, as I’ll explain later.

My center block is 18″ finished. I knew I wanted to turn it on point twice. The method is exactly the same as used for the economy block setting. This is also called “square in a square.”

And this is where the first round of harder quilt math comes in. (It’s not very hard, just a thing to learn, or store so you can look it up.) As noted in the linked post, **when setting a square on point twice, the finished size of the resulting block is twice the dimensions of the initial finished square.** For my 18″ block, I would end up with a 36″ center, once trimmed and finished. *(See below for the calculation and reason why.) *

What a great way to quickly increase the size of a quilt!

After trimming, I added a 1″ border all the way around, taking it to 38″ square. That’s an odd size.

**Options for a 36″ Edge**

Most quilt blocks are square, or are rectangular with length twice the width, like flying geese blocks. I typically divide a border length into a number of equal increments to find how many blocks could fit along the edge. For example, if I put a block border directly along the 36″ center, I would divide 36 in various ways to get possibilities. Let’s start with whole inches.

36/18 = 2. I could have 18 blocks measuring 2″.

36/12 = 3. I could have 12 blocks measuring 3″.

36/9 = 4. I could have 9 blocks measuring 4″.

36/6 = 6. I could have 6 blocks measuring 6″.

But remember we could also go to half-inches, such as

36/8 = 4.5. I could have 8 blocks measuring 4.5″.

36/24 = 1.5. I could have 24 blocks measuring 1.5″.

You can see there are actually infinite variations, though I like to stick to the ones that are easy to construct.

**Options for a 38″ Edge**

But I didn’t want to put a block border directly against the large center. I wanted the hard line of a narrow border before anything else, to contain the pale toile. That gave me 38″, which is harder to divide nicely than 36″.

38/19 = 2. I could have 19 blocks measuring 2″, but this was too narrow to work well with the proportions of the center. And 19 is a prime number, so I couldn’t subdivide it into whole numbers.

I could shift to fractionals, such as

38/8 = 4.75. Sure… This actually would work fine with something like HST or hourglasses.

My go-to blocks are half-square triangles and hourglasses. I don’t want this quilt to look like others I’ve made, so it’s good to try something different.

Then I had a thought, a math thought! What if I divide 38 by 1.414? (That actually was the first thought. Then I thought…) If I turn blocks on point rather than set them straight, I would need to know the number of blocks using the math for the diagonal.

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.)

**Pythagorean Theorem**

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; b = 1; 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″.

**38″/1.414 = 26.875″**. Hooray!!

Huh? Why is that good? 26.875 is very close to 27, which is a very easy number to use. For instance,

27/9 = 3.

**I could use 9 blocks measuring 3″, turned on point.** (There were other options, too, such as 6 blocks at 4.5″.)

3 x 1.414 = 4.242, the diagonal of a 3″ square, and the width of a 3″ block when turned on point.

4.242 x 9 = 38.178, or very close to 38″.

So if I use 9 3″ blocks turned on point, I’ll have the length needed for a 38″ border.

*(And to review the concept in another way, let’s go back to the 18″ block. When I turn it on point twice, I’m doing this:*

* 18″ x 1.414 = 25.452″*

* 25.452″ x 1.414 = 36″.*

* This is the same as 18″ x 1.414² = 18″ x 2 = 36″.) *

I chose to use the historical print and other blue scraps as the 3″ finish squares. For the background fabric, a light background would give good value contrast for the blues so they stand out well. I picked a pink and tan print on pale cream. The pink works because the reds have a pink cast. Right now I’m still working completely from stash and scraps. I was able to cut most of the setting triangles from a couple of larger pieces, but for the last few I had to sew scraps together to cut patches.

With the on-point border added, my current center is 46.5″ finished, another weird number. I plan to add an unpieced strip next, but I haven’t decided its width. I could add a strip to take it to 48″, 49″, 50″… So the next design decision, really, is the border after that, which will determine the width of the strip.

I feel really fortunate to have the math skills as part of my craft toolbox. You can make beautiful quilts without knowing how to do any of this, but knowing increases the options open to me. **Math is awesome!**