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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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## A Peek at Spring Quilt Market

If you are in the quilt business, you know to save a few days each May for the Spring Quilt Market. This industry trade show gives me the opportunity to meet shop owners and show them my new fabrics and quilt designs.  As a shop owner myself, I’m able to meet the vendors with whom I do business, to discover new products to carry in the Studio, to see old friends and make new ones.

Before market begins is something called “Schoolhouse” where manufacturers, publishers and designers like me get to present our latest products. Shop owners can hear first-hand about the merchandise they will be selling from the people who created them. I spoke about my Palette Pixie Strips and their accompanying quilts, my new calipers and, most exciting, my next fabric collection, Bedfordshire.

Once Market begins, retailers have the opportunity to visit hundreds of booths with every kind of product which could possibly be of interest to quilters. I shopped for interesting patterns and new notions to carry in the Studio and online. Much of my time, though, is spent in the RJR booth meeting shop owners and learning about their customers’ interests.

What I probably enjoy most are the wonderful people I get to meet, those whose products I sell (and use!) and other designers.

Of course, one of my favorite things to do is looking at all the quilts. Even though I have been designing fabric for many years, I still get a thrill when I come across quilts in other booths which have my fabrics in them. Here are two I spotted. Didn’t these quilters do a wonderful job?

Inspiring.  That’s the word I would use to sum up Market. The room was filled with a creative spirit. Handwork seems to be celebrating a resurgence. It was exciting to see this interest in a skill you and I have loved for years.

Also, I was so encouraged to see the number of young people there who have entered the business presenting their designs and products. They give the industry a sense of vitality and reminded that quilting should be FUN. Yes, market is always inspiring and I’ve brought back some new products and ideas I can’t wait to share with you in the coming months.

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## Quilter’s Design Board

How many of you have never played around with our Design Board? Did you know that there are 223 free patterns in three different sizes (6, 10 and 12 inches) and that a new pattern is added each month?

The blocks are grouped by how they are drafted such as 4-patch, 5-patch, 8-pointed star, etc. First, choose a block. You can print out templates for three different block sizes along with a template guide. Then the blocks can be put into a quilt and borders can be changed. There is a yardage calculator that gives the style numbers of the fabrics used in the block and also will determine how much fabric you need based on how many and what size blocks you want to use. It will even give you an estimate of the cost and put your fabrics directly into your shopping cart.

This months’ block is Golden Tile. First and foremost, the block gets its name because it contains the Golden Proportions as was explained in a recent blog post. If the Golden Gauge Calipers are opened so that the smaller space fits on the shorter segment of the design, the larger opening fits on the longer segment.

The design board is limited and is not meant to take the place of your graphics program but serves as a jumping off point. There are some wonderful software programs available which provide you amazing design possibilities. For blocks such as Golden Tile which are directional, you do not get the chance in the design board to see some of the other possible layout variations. If you have a graphics program that allows you to tile, rotate and flip blocks, experiment with different layouts. Here are some variations.

I hope you take the chance to play around with our Quilter’s Design Board and don’t forget to send us pictures of the quilts you make from it.

P.S. Golden Ratio by accident or design?

Dana, our staffer who did the layout for the blog sent it to me for approval. As soon as I saw her layout, I couldn’t help myself. I had to get out the calipers. So often when we are doing design or layout work, we select the proportions that are most pleasing to us and so many times it seems to fit the proportions of the golden ratio!

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## Make Way For Goslings

Well, we almost had a disaster at the Beyers Monday morning. We have a pond on our property and every morning when I let out Gus and Luke (our two labs), we walk around the pond together. As we were coming along the dam, two adult geese suddenly flew from the sky, dive-bombed the dogs, then landed in the pond. Seconds later, another pair streaked up the dam and flew into the pond, all of them honking furiously. The dogs, of course, thought this great fun and went in after them.

Then, out of the corner of my eye,  I caught sight of a group of five precious little goslings on the slope of the dam. I knew if the dogs saw them the goslings would be completely vulnerable.  I yelled at Gus and Luke that it was time to eat and started running to the house. That got their attention and they jumped from the pond to follow me. (Well, they are labs, you know, and when you mention food…)

A few minutes later when I went to get the newspaper, I met my neighbor, Kim, who was carrying a camera with a huge lens. She said she was on her way to photograph some baby foxes she had seen. (Is my neighborhood starting to sound like that old TV show, “Wild Kingdom”?) I told her of the near miss with the goslings and invited her to come take a look. We could check to see if all the geese were okay.

When we arrived back at the pond, there were the goslings swimming along with their parents. Kim got some great photos and when I saw them, I couldn’t help thinking about the blog post two weeks ago which explained how to get colors out of a photograph. I couldn’t resist so here they are.

The colors immediately reminded me of the version of Crayon Box that is made with the “tropical” set of Palette Pixie Strips. The only thing missing is the blue sky which was there but just didn’t make the photo.

I suppose I just can’t help myself from seeing color palettes, fabric designs and quilt possibilities all around me. I hope you are letting your world inspire you too.

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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.

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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## How to Get a Quilt Book Published…By Accident

People often ask me how I got into writing books. The first one came as a fluke and the others just fell into place.

I started teaching patchwork to small groups in my home in the mid 70’s and there were very few quilt books or patterns available. If you wanted a pattern for a quilt you had to draft it yourself. I figured out that most square patchwork designs were based on a “grid”. The square was divided into a grid of 3 x 3, 4 x 4, 5 x 5 etc. If you knew what grid was used for the block, it was simply a matter of following the lines of the grid to get the design.

I figured out a no math way to fold paper to get the designs and after teaching it for a few years people were amazed at how easy it. Let’s use the block above, a 4×4 grid which is simpler than it seems. Decide what size block you want and make a square that size out of paper. Fold the square in half, side to side, then in half again, bottom to top. This will produce a “grid” of four squares. Can you see now how the design is created? If not, fold it in half each way again. Now you can see that is made up of simple half-square triangles.

So one day, my Quilters’ Newsletter magazine arrived and in it was an article on how to draft an eight-pointed star. It talked about the Pythagorean Theorem, pi and all sorts of other math terminology. I was completely confused, particularly since I had figured out a very easy way to draft the design by folding paper.

I wrote a letter to Bonnie Leman, founder and editor of Quilters’ Newsletter, and showed her my method. In a rash moment, I also wrote, “Furthermore I’m explaining this and how to draft other patterns in the book I am writing on pattern drafting.”

Bonnie phoned me when she received my letter and said how she was so excited about my book and who was publishing it? I kind of hemmed and hawed and said I didn’t have a publisher yet. She said that she might be interested in publishing it and could I bring what I have done so far to a conference we would both be attending the next month. I didn’t want to tell Bonnie that I hadn’t actually started the book, so for the next month I prepared outlines, did illustrations, wrote sample chapters, etc.

While it turned out to be a larger project than Bonnie imagined, she encouraged me to find another publisher, and I did. My first book, Patchwork Patterns, had 500 patterns and was organized in categories according to the grid used for drafting them. The book is out of print and I’ve written other, more comprehensive ones since, but that one is still special to me. So that, my friends, is how you accidentally get a quilt book published.

An upcoming blog post will show you how to figure out the grid.

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Spring is in full swing here in northern Virginia. How do I know this? Well, it could be the warmer temperatures or cherry blossoms blooming. But it’s not. For me, I know it’s spring because my 14-month-old dog, Luke, has been trying desperately to catch a frog since they have reemerged with the nicer weather.

We have always had dogs. I like having two. The older dog teaches the younger one and they keep each other company. Luke is our newest puppy. He came to cheer Gus up after we lost our Swissy, Gretchen. I have to say that Luke is one of the funniest dogs we have ever had. I will not be able to resist periodically sharing some of his and Gus’s antics.

However, for most of you, spring is about warmer temperatures and whatever it is you have blooming around you. I’m very fortunate that I live close to the Potomac River. I walk along the river three or four times a week. Monday of this week had to be the most gorgeous day of the year. Greeting me was a spectacular array of native flowers—bloodroot, toadshade, Dutchman’s breeches, toothwort.

The most amazing, though, were the Virginia bluebells which were at their peak. There was a carpet of bluebells stretching into the woods as far as one could see and reaching in the other direction to the banks of the river.

I came back fully inspired.

I often take colors from nature and use them in my quilt and fabric designing. Here are the colors of the Virginia bluebells.

I think these colors make a beautiful palette for a quilt. How did I get them from the image? It’s pretty simple if you have Photoshop.

1. Open the image in Photoshop.
2. Go to the top menu bar to Image/Mode/Indexed Color. Select the number of colors you want to see from the pop-up menu. You can go up to 250.
3. Next go to Image/Mode/Color table. The chart with all the colors will come up.

Once you can clearly see the colors in the image, it is easy figure out your fabrics. I’ve used my Portable Palette which has swatches of all 150 of my Palette fabrics.

So take a walk and get inspired. Oh, and Luke? He’s still out there trying to catch a frog.

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## Me & Heartbleed

Although I use a computer all the time when designing my fabrics and quilts, my staff will be the first to tell you that I’m not really a very technical person. So all the chatter about the Heartbleed bug on the internet had me confused and concerned.

Fortunately, I have very good technical people working for me and they were able help me understand what was going on AND take care of the issue quickly. I thought you might be interested in what I learned:

1) Heartbleed is the name given to a bug in a key piece of internet security software that about two-third of websites use — including jinnybeyer.com.

2) The bug was discovered BEFORE any known attacks were made taking advantage of that bug.

3) Most banks and financial services companies, and some super-big online stores such as Amazon, were never vulnerable to Heartbleed.

4) The bug is relatively easy to fix.  Many large websites (such as Google) have already made their fixes. We made the fix to jinnybeyer.com last week, on April 11. I knew that we do not store credit card information on our website and was relieved to learn that the company which takes care of that for us was never vulnerable to Heartbleed.

5) Some security experts are suggesting changing passwords on websites once the fix has been made to that site. As a result, we are suggesting to customers who have accounts on jinnybeyer.com that they change their passwords.  If you have an account on jinnybeyer.com, you can change the password here.  And I guess I’ll be changing passwords on some of my favorite websites, too!

I love what technology brings to my quilting world, and I’ve certainly done my share of shopping online. But I really do wish that we could somehow get only the good from the internet and not all the negative possibilities.  That being said, I am grateful to my crack staff who keeps me in the know on these issues and to the people and companies I rely on to keep our website running safely and reliably.

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## Yesterday, Today, & Temari

I have an incredible group of people who work at the Studio. It is always hard to find suitable ways to tell them thank you for all they do. It is particularly hard at holiday time to come up with an unusual gift.

Last fall, my husband’s college roommate and his wife came for a visit and stayed with us for a few days. The woman loved my quilting and shared that she was a temari ball maker. She brought up several web sites and showed me photos of balls she has made.

How could a quilter not be enthralled with these amazing geometric pieces of art? I was definitely intrigued. I went to Quilt Market in Houston shortly after their visit and my publisher had a couple of temari ball books written by a well known temari ball maker, Barbara Suess.

Bottom line, I decided to invite Barbara to come teach at my shop for two days. One day would be for the general public and the other day would be a special workshop for all my staff. I decided that this would be a perfect Christmas present. So when we had our holiday staff dinner, I presented them with Barbara’s book, Japanese Temari, gave them a Yazzi bag to house their Temari project and told them the date of the workshop.

We had the workshop last week and it was fabulous! Barbara and her two protégés were wonderful instructors.  Starting with a knee-high stocking filled with rice hulls, the wrapping then began, with yarn first followed by thread. Soon the design took form with colorful perle cotton. Kristi finished her ball first and I made the biggest mess. We all had a great time and each of us produced a beautiful temari ball.

If you have made any of my patchwork puzzle balls you will definitely be intrigued by these.

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## Welcome to My Blog

I’m so excited to launch my blog, Jinny’s Corner!  Each week we’ll share news, tips and techniques, stories and other quilting-related information.  I hope you’ll visit here often.

Since this is a new feature, I thought I would answer some questions that you might be asking.