Tag Archives: Center block

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.)

Sq_rt_of_2
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.

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A Lot of Fun Stuff Going On

It’s been a while since I’ve showed you my current work. A couple of weeks ago I finished binding a project started last year. It was the one that made me tear my hair out, along with thousands of quilting stitches. It’s finished, but it’s for a loved one and I’d like to get it to her before showing it off here. Just in case.

If you’ve been a reader for a long time, you may have noticed (or seen me write) that I often don’t post about projects in their early stages. Mostly that’s because I don’t much like taking pictures, and it’s hard to describe a project without them! The project I’m working on now is much the same. I actually started it months ago, and now finally am getting around to posting. This time, however, it really still is in the early stages.

So what’s been done so far?

  1. made 112 flying geese to use in a strip quilt
  2. found and pieced together a long strip of border stripe, to use in said strip quilt
  3. changed my mind and decided to use the geese and the border stripe for a medallion quilt
  4. drew house block to center the medallion
  5. sewed house block
  6. embroidered embellishments on house block
  7. framed house block to stabilize it and standardize the size
  8. prepped border stripe (most of the way) to serve as the first showy border

I began the flying geese as I finished making Union. As mentioned before, I was still enjoying the double pinks and browns, and I wanted to combine them with reds, aquas, and teals. Since the fabric was still out, I started cutting pieces for the four-at-a-time method of making geese units, but I didn’t start sewing them until this year.

I’m not sure what inspired me to make a medallion with a house center block. I’ve always been charmed by folk art including early American embroidery samplers, which often featured houses or school buildings. Recently Barbara Brackman posted about quilts with yellow house motifs. Maybe that got me going. I also had a hard time imagining the strip quilt I originally intended. I couldn’t figure out the numbers of strips or what, besides the flying geese, to use. It seemed like it would be a lot more piecing than I wanted, and perhaps without a good enough payoff.

At any rate, I drew that house.

Sometimes the easiest way to do things is the old-fashioned way, and here graph paper and pencil worked just fine.


I’ll show you what happened from there next time. Before that, the title of this post might merit some explanation. There IS a lot of fun stuff going on, which is good, since one of my primary intentions this year is to have fun.

I’ve had lots of RPT (Real People Time) already this year, and a lot more coming up. On Thursday I’ll have lunch with a dear friend from grad school. She and I lost touch several years ago, and it will be a treat to catch up.

Guild stuff keeps on comin’! Between the presidenting and committee-ing and bylaw reviewing, there’s always enough to keep me busy. Besides that, I decided to go to the three-day retreat in mid-February. That means I have to FIGURE OUT WHAT TO TAKE to keep me busy for three day!!! ACK! So much fun! 🙂 (Imagine that smiley face with a slightly crazed look to the eyes.)

I’m also doing things in my non-guild quilty life that are new and different, but things I’ll wait to explain. Could be a crazy year with that, too.

I updated the blog a bit, gave it a little fresher look. My galleries are finally up-to-date, after languishing without much care for too long.

And then the other personal stuff, including travel coming up. We have four trips pegged already this year and forgive me for hoping that’s all we do!  But really, Son’s wedding? FUN! Granddaughter’s graduation? FUN! And a couple of trips for fun? FUN!!

Okay. That’s enough for this time. I’ll show you more of my house project in the next post.

 

Class Quilts

My medallion class began last week! In class I help lead participants through the process of designing their own medallion quilts. And while they create, I do, too.

In the few weeks we have together, while each of them is making one quilt, I design and construct two. I start with very different centers and color schemes in order to demonstrate a variety of strategies.

The first one I began has a center block that features flying geese circling a star. The block design came from the Big Book of Scrap Quilts, published by Oxmoor House in 2005. The quilt pattern is called “Dizzy Geese,” designed by Joan Streck. Dizzy Geese is a block quilt, with a 17″ block made with templates.

I re-drew the block to 16″ and paper-pieced it.

Though I’ve made quilts in reds and greens before, I haven’t made one I’ve thought of as a Christmas quilt. This one will have that intention, but I’d still like to keep it lighthearted. I’ll minimize the holiday-focused prints, but refer to the occasion through shaping. For instance, the circling flying geese give the impression of a wreath.

With the intricate center, I wanted a simple first border, but one that would extend the range of color. Because the star points are a forest green print, I chose a citrus green for the border. The corner blocks add to the gold, found in the center’s green print and in its background fabric.

The second border was fun and easy to make. Take a look. The corners are just half-square triangles. The side blocks are each made of three pieces and all the blocks are same. Their orientation gives the look of a twisting ribbon as they circle the top.

And the third border is a plaid with dark green, dusky gold, and burgundy, with bright gold corners. I don’t love the dark plaid, for various reasons. But I think it will serve its purpose as the design develops. It’s easy to get hung up on individual elements, such as the color or shapes or value of a particular border. Just as you don’t have to love a particular block to have it work well in a block quilt, you don’t have to love a particular border in a medallion quilt. Every border changes every border, and it’s the final effect that counts.

I have tentative plans for the next borders, but won’t work on this more until next week.

The second quilt begins with a bear’s paw block in the center. I’m less certain of the direction for this one. I really like the center block, with its beautiful Julie Paschkis print in the large sections. And I love the batik that surrounds the block. I am not absolutely sure they work together. However, some patience is in order as I let the process play out. (Trust the process.)

Though I rarely work on two quilts in the same stage at the same time, the chaos is kind of exciting, too. We’ll see if I still feel that way in a couple of weeks. 🙂

Turning a Block On Point Twice

Friday Jim and I drove down the Mississippi River from La Crosse, WI. We were returning from a two week trip to see our son, who lives in Washington state. With 2,000 miles behind us on the train, it felt great to switch to our own car.

In Prairie Du Chien, WI, we stopped for lunch. On one wall of the diner hung a quilt with a patriotic theme. It was a medallion quilt, centered by a stylized American flag. The flag block was turned on point twice, emphasizing its importance and creating a nice, large center.

I liked the setting, and especially liked that a non-square rectangle was turned that way. It’s a setting I haven’t used myself.

I’ve written plenty about turning large blocks on point to center a quilt. In one post I described the types of blocks suited for an on-point setting, if it is only turned once. In another I showed how to do that, with the math needed to cut your setting triangles large enough. I’ve also written about turning small blocks twice, creating an “economy block.”

But I’ve never written about turning a larger rectangular block twice. Here are some cool things I learned about it.

*~*~*~*~*

The Part I Already Knew
If you turn a square block twice, you’ll double its dimensions. Consider an example of a 15” block. Turn it twice with an exact (not over-large) setting, and you will create a block that is 30” wide. Using the math for diagonals,
15” x 1.414 = 21.21”.

Now turn it again:
21.21” x 1.414 = 30”.

This block setting is often called an “economy block.” It’s an especially effective way of highlighting a small centerpiece, such as a special or fussy-cut piece of fabric.

Economy block setting – a square turned on point twice.

The Part I Didn’t Think About Much, But Probably Knew, Too
As it turns out, you can do this with non-square rectangles, too.

Non-square rectangle, squared first with unequal triangles, and again with equally-sized ones.

The Part I Didn’t Know, And Figured Out Last Night
The size relationship for both types of blocks can be generalized, and is far easier than multiplying by 1.414. If the length of the inside shape is A, and the width of the inside shape is B, the distance across the diagonal of the interior square is A+B. That means the length of the exterior square is A+B.

In the economy block example above, the interior square is 15”.
The resulting block is 30” square, or 15” + 15”.

In the second example, if the interior blue rectangle is 12” x 18”,
the resulting block is 30” square, or 12” + 18”.

The next time you want to frame a rectangle with setting triangles, remember how easy it is to determine the finished size. Length plus width of the interior rectangle (square or not!) is the width of the resulting square.

Ain’t math fun? 🙂

Medallion Quilt Rules

Each year my local guild has a new challenge, and I’m excited about this year’s! The current challenge is to create a medallion quilt. Though I won’t enter, I’m looking forward to seeing the entries and hearing from members as they create their pieces.

We just started our guild year this week, and it will close out in July with display and judging of these quilts. To help my fellow members move through the process, and also to help and inspire others who want to make medallions, I’ve decided to republish some of my prior posts. The best place to start is the beginning, right? Below you’ll see the fundamental rules of making a medallion quilt.

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