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## Golden Ratio and Nature

One day I was walking along the Potomac River near my home and met a man who was studying one of the plants with great interest. I asked him what was so fascinating about the plant. He told me that the name of the plant is Horse Tail and that he was very curious about the sections of the stem and how they seem to follow some sort of pattern. I took one look at the stem and immediately knew what it was. Then I also realized that I had the same plant growing in the fish pond in my yard. I was anxious to get home and see if my theory was correct.

Several times in the past I have written about the Golden Ratio (also called the Golden Proportion, Golden Mean, Devine Proportion or Phi) . Its appearance in nature, design and the entire universe is uncanny. It is the division of a line segment where the ratio is 1 to 1.618. One is the shorter length and 1.618 the longer one. BUT it is also the ratio of .618 to 1 where .618 is the shorter segment and 1 the larger. This is what makes this ratio so magical.

Now I know that the mention of proportions, ratios or anything mathematical can make the eyes of most people roll back in their heads (unless you are a math geek). So, a few years ago, I designed a set of calipers for quilters that open up into these pleasing proportions of the Golden Ratio. I got them out when I returned home from my walk and took one of the Horse Hair stems from my pond and tried them out. Sure enough, when I place the calipers along one of the longer sections, the shorter piece next to it fits the proportions of the Golden Ratio and vice versa. One note, the sections at the base of the stem don’t quite fit into the ratio, but they fit more perfectly as I reached the tip of the tip of the stem. It is fascinating for me to see how this proportion shows up in so many aspects of our world.

Go to the blog section of my website and do a search for Golden Ratio or Calipers and read what I have previously written about this proportion and how we can easily apply it to quilt design.

Do an internet search on the Golden Ratio and you will be amazed at what comes up about this magical phenomenon.

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## Golden Ratio and Proportions for Borders

A comment on one of my recent blog posts asked a question about how to use the Golden Gauge Calipers and the Golden Ratio in choosing borders for quilts.

For those of you not familiar with the Golden Ratio or the Golden Gauge Calipers that I designed see these blog posts. Or just search “Golden Ratio” on the internet and be prepared for a wealth of information.

The Golden Ratio is thought to be the perfect proportion for all sorts of art and even in nature.  The ratio is 1 to 1.618 or 1 to .618. The calipers open exactly to that measurement and save the math. I’ll show you here how I planned the border for Wings.

I wanted the first border to be the same size as the frame around the hexagons. That frame is ¾ inches wide. But how wide should the second border be?

I placed the calipers on the first border with the small opening across the ¾ inch. The wider opening gave me the size that would be a good proportion for the next border.  That measurement was 1.21 inches. I just rounded up to 1 ¼ inches.

Now, I had two choices for the last border. First I could put the smaller opening of the calipers on the red and the larger opening would give me the size for the final border.  Or, if I wanted a wider border I could put the small opening of the calipers on both of the first two borders and the outer border would be wider.

Here is the image of both variations of the border. I felt that the design was so bold that the wider one looked better. But in either case, there is a pleasing proportion between the widths of the borders, no matter which one you use.

Give it a try!

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## Fibonacci and the Golden Ratio

A few blog posts ago, when I talked about the Golden Ratio, (1 to 1.618 or .618 to 1) there were several questions about how the golden ratio relates to the Fibonacci number sequence.

Leonardo Fibonacci was an Italian mathematician (c. 1170-1250) who devised a number sequence where the relationship of one number to the next or previous one provided perfect proportions. Mathematicians and artisans have been using this number sequence ever since. Some quilters use these numbers to plan proportion for their designs.

Fibonacci’s number sequence goes like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

Can you see how the numbers are determined? Here’s how the sequence works. Start by adding our first two numbers: 0+1=1. Go to the second and third numbers, 1+1=2, then 1+2=3 and so on. Each successive number is the sum of the previous two numbers.  You can select any number in the sequence. It is always the sum of the previous two numbers.  For example 21 is obtained by adding 8 and 13.

But in actual fact, this is virtually the same as the Golden Ratio.  As the numbers get higher the relationship between two adjacent ones approximates the golden ratio.  In fact from the 10th number on, you will get a value of almost 1.618 or .618 every time!

The rectangles and spirals shown here, illustrate exactly how the Golden Ratio relates to the Fibonacci sequence of numbers.

Fibonacci Spiral:
Fibonacci begins with two squares, (1,1,) another is added the size of the width of the two (2) and another is added the width of the 1 and 2 (3). As more squares are added the ratio of the last two comes closer each time to the Golden Proportion (1.618 or .618). Put quarter circles in each of the squares to get the Fibonacci Spiral.

Golden Spiral:
The Golden Spiral begins with a square and a rectangle is added whose width is .618 of the first square. Another square is added that is the width of the first square and rectangle (1.618) This proportion continues so that all the relationships are either .618 or 1.618. Once again the spiral is achieved when quarter circles are drawn in each of the squares.

Comparison of the two spirals:
An overlay of the two spirals shows that at the beginning they do not match up but as Fibonacci’s numbers grow the two spirals are virtually the same. The Golden Gauge Calipers show that the spiral is in perfect Golden Ratio proportions, 1 to 1.618!

All of this fascinates me. And I discovered that you can do the same type of number sequence starting with a different number. For example, we can call this one “Jinny’s Sequence”.

3, 3, 6, 9, 15, 24, 39, 63, 102, 165, etc.

Once again, by the time you get to the 10th number, and divide the 10th by the 9th you get very close to the Golden Ratio….1.6176

It seems to come out this way no matter which number you start with. So you may be asking yourself, do quilters really use this? My quilt, DaVinci was something of an ode to the proportion with the strip widths determined by this mathematical ratio.  I am a huge fan of the work of Caryl Bryer Fallert, who has created an entire Fibonacci series of quilts. Why don’t you give it a try?

If you find all this fascinating check out the previous blog posts on the Golden Ratio.

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## The Magical Golden Ratio

It’s been said that the golden ratio (also called the golden proportion, golden mean or Phi) is the perfect proportion. The golden ratio certainly seems to have magical properties. It occurs in nature, in the human body and in animals, in ancient art and architecture, even in many of our quilt designs. Let’s do a little test. Pick out the illustration you find the most pleasing in each row.

I have given this test many times over the past decade and usually 75% will pick A, B, and B. If you picked these, you picked the shapes which have the Golden Ratio. So what is the golden ratio? OK, here comes some math. (Warning! Your eyes may be in danger of glazing over and your mind may wander. Never fear: it is only two sentences long.) It is the division of a line segment where the ratio is 1 to 1.618, one being the shorter length and 1.618 the longer one. It can also be the ratio of .618 to 1 where .618 is the shorter segment and 1 is the larger.

Most spirals found in nature fit the proportions of the golden ratio.

You will find that this ratio has been used throughout history. Some examples include the Greek Parthenon, the Great Pyramid at Giza, the paintings of Leonardo DaVinci. However, a truly fascinating aspect of this magical ratio is that it occurs so often in nature. For example, in a beehive there are fewer male bees than female bees. The ratio of males to females is the golden ratio! A pinecone has two sets of spirals, one with less spirals than the other…..the relationship between them is again the golden ratio. Look at the photos above of the shell and Romanesco broccoli as another example. The golden ratio is even evident throughout the human body, in the measurement from the top of the head to the chin and from the chin to the navel and from the navel to the floor. Measurements from the elbow to the wrist and wrist to the tip of the middle finger also fall into the golden proportion. If you are like me, you don’t like carrying a calculator around all the time and doing math, but you might be curious as to the proportions of various objects. Because of this I developed the Golden Gauge Calipers. This is a handy tool that eliminates the math and lets you see the golden proportions in objects. As the calipers are opened the shorter segment in relation to the longer one is the golden ratio and vice versa. When the calipers are opened so that the narrow space is the size of the width of oval A you will see that the wider portion of the calipers is the height. The same is true with triangle B. If you open the calipers to the narrow portion across the base of the triangle, the height will be the space between the wider portion of the calipers.

With the calipers on the Mariner’s compass B notice that the width of the smaller center circle is in “golden proportion” to the distance from the edge of that circle to the edge of the larger circle. Many patchwork designs contain divisions that are either very close to or exactly the golden ratio. Are designs with golden proportions more pleasing to the eye?  Take a look at Duck and Ducklings and Whirling Five Patch, shown here. It is apparent that the designs have the same basic pattern. The difference is that one is drafted on a 5 x 5 grid and the other on a 14 x 14 grid. Which one is most appealing to you? I personally find Duck and Ducklings a little clunky and like the fact that Whirling Five Patch contains divisions that are not all the same. The Golden Gauge Calipers placed on the design shows that the width of the center division to the adjacent one almost fits golden ratio proportions.

Unknowingly, quilters when planning widths for borders automatically choose this proportion because it “feels” right. In one of the upcoming blogs we will take a look at borders and how to determine a pleasing size.

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## Protea – A Bundle With So Many Possibilities

Last month, we introduced our latest grand bundle, Protea, named after an amazing flower found in South Africa. As I often do, the colors for this bundle we’re pulled from a photograph the Studio’s manager, Rebecca, took while on a trip there in 2017. If you are interested in this process of capturing colors from a photo, I wrote about it in a blog when we introduced the Irish Heather bundle.  There are 40 fabrics in the Protea bundle and we have broken it up into five smaller bundles of eight fabrics each. Once a month we offer one of the smaller bundles as our web special.

Whenever we introduce a new bundle, we always discuss possible projects to give you all an idea of how you can use the fabrics. Both the Thousand Pyramid and Tumbling Blocks quilt were shown in the Irish Heather blogs and would be perfect for this bundle as well. Another suggestion is a quilt, Potomac Charm, designed in 2013 for the Quilters’ Quest shop hop.

Potomac Charm used 99 five-inch charm squares so, in order to have enough to play with, we cut two squares from each of the 40 Protea fabrics and staffer Nancy and I started arranging them on the design wall. We decided on a setting of 54 “blocks,” set six across and nine down. Swatches were added, moved around and taken down. Just when we thought we had it set we would change it again. Then we added border prints down the sides to audition them. What do you think?

After the positioning of the squares was set I created a digital image and played around with border options. Since the quilt was so small, I chose to start with the narrow border from the Casablanca fabric. The best outer border was just a wider black piece. To determine the best width for that last border I got out my trusty Golden Gauge Calipers. This gave me the perfect size for that last border. If you are not familiar with the Golden Ratio, check out my blog on this topic from a few years ago.

I tried another version using the border print from Miyako.

The finished quilts are approximately 59” x 67”. We always have people wanting to make our quilts larger. So I decided to play around with the digital image. I removed the top and bottom rows of squares then made two exactly alike and two that were the mirror image.

Since the quilt is larger, I used the wider stripe from the fabric and then used the calipers to determine how wide the black should be. Here is the quilt with the two different borders.

No longer a charm quilt (charm quilts do not duplicate fabrics), we decided to name this Protea Squares. The small quilt measures 34” x 50.5” without the borders and 59” x 67” with the borders. The large quilt is 67” x 78” without the border and 84” x 95” with the borders.

The finished width of our smaller quilt outer border is 3 7/8” (cut 4 3/8”). The finished width of the larger quilt outer border is 8½” (cut width 9”).

We are giving the Potomac Charms pattern here as a free download. You can use that as a guideline for creating your own 5” square quilt. We encourage you to play with fabric placement and settings, adding more squares or less, (depending on the size you want) or even adding fabrics from your stash.  Once you get started, I’m sure you will have as much fun as we did.

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## And the winner is……

Back in the beginning of May we announced a contest inspired by a box of packets of 10-inch squares from last year’s Quilters’ Quest. We challenged you to design and make a quilt (or quilt top) using these fabrics. Photos had to be submitted by June 18th.

What fun we had looking at your entries! Each member of the Studio staff, totally untrained in any kind of quilt judging, voted on his or her favorite.  The quilter who got the most votes wins a \$100 Studio gift certificate.

About a dozen people managed to finish their projects and submit them in the short amount of time given. There was a wide range styles and entries came from around the world.

And the winner is…Sarah Kirtland from Williamsburg, Virginia.

Sarah’s quilt, Here Comes the Sun, is based on the classic kaleidoscope block. She knew she wanted to do something with triangles after seeing my new Thousand Pyramids quilt. She spent four days simply drawing, working on the design. Sarah was at the Studio at the beginning of the month taking a class and picked up a few fabrics to supplement the 10-inch squares. Then the fiendish sewing began and didn’t stop until shortly before the deadline. She didn’t believe she had a chance to win but thought it would be a good exercise. I’m reminded of a saying by Mark Twain: “…you will be more disappointed by the things that you didn’t do than by the ones you did do.’

There were many other fabulous quilts. Here are just a few.

David Schulz took inspiration from local Native Americans who had different names for different parts of the Potomac, calling the river above Great Falls, where the Studio is located, “Cohongarooton”, meaning “honking geese.” He included flying geese blocks along with a variation on a block design from my Quilter’s Album of Patchwork Patterns (Island Compass 380-11).  He also used the Golden Ratio throughout the piece. Even the number of flying geese is included in the Fibonacci sequence. The finished piece measures 29” x 18”.

This Phoenix quilt came from Charlie MacDonald and we enjoyed his description of the process, the trials and tribulations. He loved the palette from the Quilters Quest. It reminded him of sunset/sunrise “and somehow the colors got him thinking of a Phoenix rising in flame from the ashes.” He used his Apliquick tools for the appliqué. Charlie said he learned a lot from making this and already has ideas for Phoenix 2.0.

Tom Dengler took an interesting approach. He writes: “I was inspired to find a way to challenge myself to use both sides of the fabric based on some ideas I had first seen used in watercolor quilts. The white gives the illusion of piercing the fabric by piecing the fabric backside. I learned that hand stitching the corner first gives a much neater appearance.” It is called Dos Rayos de Luz.

One thing that I particularly loved seeing was how many truly challenged themselves to try something new and, it seems, are very glad they did so. Here are more of the wonderful projects we received pictures of. We have no stories to go with them but I want to thank each and every one of you for participating and congratulations to all for your beautiful work.

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## Proportionally Perfect

If you have been following my blog, you know that I am fascinated with the Golden Ratio. The Golden Ratio (also called the golden proportion, golden mean or Phi) is often referred to as the perfect proportion. It occurs in nature, in the human body and in animals, in ancient art and architecture, even in many of our quilt designs. Did you know that ratio of the width of the credit cards in your wallet to their height fits the Golden Ratio? And I know it sounds odd, but even the stock market trends conform to it. Go to http://bigcharts.marketwatch.com and pull up the five year chart. Note that the distances between the large dips and rises fit the proportions of the Golden Ratio………hmmm.

Designs with golden proportions more pleasing to the eye and quilters often choose designs with this proportion because it “feels” right.

We recently found this fascinating video which gives you, without words, a look at the Golden Ratio, how it works, and how it is found all around us. I encourage you to take a look at “The Golden Key” by Jonathan Quintin. It makes you forget that the Golden Ratio is all about math!

After, you may want to look back at my blogs, “The Magical Golden Ration” and “Fibonacci and the Golden Ratio.”

Not to get too technical but the Golden Ratio mathematically is 1 to 1.618 or .618 to 1, that pleasing proportion we talked about earlier that we are drawn to in designs because it strikes us as being right. I developed the Golden Gauge Calipers because, though no one believes me, I’m really not fond of doing math. This is a handy tool that eliminates the math and lets you see the golden proportions in objects.

We put them to the test on several quilts and even one of my new Safari fabrics.

Artists and craftsmen and designers of all disciplines use the Golden Ratio in their work whether purposely or just because it feels right. So whether you are looking for the perfect proportion of the height of a rectangle to its width, the width of one border to an adjacent one, the height of a vase to how tall the flowers that go into it should be, give the proportions of the Golden Ratio a try.

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## The Row by Row Experience 2015

The Row by Row Experience has begun!  If you are not familiar with the Row by Row Experience, it is similar to a shop hop, but a bit different– no fees, no cards to stamp, and you have all summer to participate. Simply visit any of the participating shops throughout the USA and Canada and receive a free pattern for a row in a quilt. Combine your rows in any way to create a unique quilt that represents the fun you had traveling throughout the summer. This year’s theme is…..water.  Each shop has created a row based on this theme.

The Studio’s row is based on the nearby Great Falls National Park. At Great Falls, the Potomac River builds up speed and force as it falls over a series of steep, jagged rocks and flows through the narrow Mather Gorge creating its spectacular falls. The row represents that series of rocks and rushing white water. It may look complex but it is actually very easy to piece with simple paper piecing techniques.

Create a quilt using at least eight different rows from eight different participating shops and be the first to bring it into one of those participating shops to win a stack of 25 fat quarters. If you are the first to bring a quilt into the Studio, those 25 fat quarters will be your choice from our entire stock of fat quarters. And if you use the Studio’s row in your quilt, you will win a bonus prize—Golden Gage Calipers!

Why calipers? There is an interesting reason why we chose them.  After our sample row was entirely put together, I made a discovery. Unknowingly and without trying, my design conforms to the Golden Ratio. The Golden Ratio, which occurs in nature, ancient and historic design, is said to be the perfect proportion. It is the ratio of 1 to 1.618 or .618 to one. When I put the calipers on our row, I saw that each triangle increases in size according to the Golden Ratio.

Besides the free row pattern, we have some special products.  Row kits with all the fabric needed to complete our row and fabric bundles in the gorgeous fabrics of our row will be available. Not only do we have fabric license plates with our slogan, “Perfect Piecer,” but we also have collectable pins. Watch for more products based on our Great Falls row.

Row by Row runs through Tuesday, September 8th. Stop in when you are in the Washington, D.C. area or take a road trip with friends to discover new quilt shops and old favorites and have fun collecting your rows.

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## My Visit to India

Wow! I’ve just arrived back from another whirlwind tour of India with Sew Many Places. Jim West certainly knows how to put together an exciting and educational adventure.

We rode on bicycle rickshaws through Old Delhi and Jaipur, motor scooters, buses, camel carts and elephants. The dates of the trip were planned around the Festival of Diwali (known as the festival of lights) and the Pushkar camel fair.

I began quilting while living in India years ago and every time I go back I am inspired anew by the color and design that surrounds this incredible country.

Words cannot describe what all we did and saw, so I thought this blog should be more photos than words.

Meanwhile, I have three more exciting trips next year……..to Costa Rica, Tuscany and Bali. I would love to have you join me on another adventure.

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## Gardens Gone Wild

I swore I wasn’t going to dwell on my vegetable garden this year, but I just can help it. It is going crazy!

My corn is way taller than an elephant’s eye (I’m 5’6”).

I can’t reach the sunflowers.

The tomatoes, which were slow to ripen, have now all decided to turn ripe at the same time. I have to beg people to take zucchinis and cucumbers.

We are enjoying my favorite tomato salad every night. (See my recipe below). And then just this morning I saw some red ripe tomatoes way inside the plant. When I reached for the first one, I realized it wasn’t several but just a single gigantic one. It weighs 2.68 pounds! While I realize that is not the world’s largest tomato, I think it is pretty big and I wasn’t trying to grow a large tomato.

I have used my Cuisinart so much that it died on me this morning while I was in the middle of making 10 quarts of tomato sauce.

Let’s get back to my sunflowers for a moment.

Notice in this close-up that the seeds form a pattern of two sets of spirals going in opposite directions. If you count the two sets and divide one number by the other, you will have either .618 or 1.618…….the golden ratio!  Also if you count the number of petals on a sunflower; it will almost always be one of the Fibonacci numbers.

Slice as many tomatoes as you need and place a piece of fresh mozzarella cheese on top of each one. (Buffalo mozzarella is the best, if you can find it.) At this point, most recipes call for putting a basil leaf on each tomato slice and drizzling with olive oil. We like it better with some fresh pesto on top of the mozzarella. I make a larger batch than I need and keep the rest in the refrigerator for use the next time. It keeps well for at least a week.

Two cups fresh basil leaves

Two cloves of garlic

¼ cup pine nuts, walnuts or pecans