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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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## 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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## 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

Dash of salt

Pepper to taste

Chop nuts, garlic and basil in a food processor, while the processor is running add olive oil in a slow drizzle until pesto forms a soft paste.

Happy eating!

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## Potatoes!

You are probably now checking to see if you clicked on the wrong thing because you were expecting something about quilting. I’ve been writing about somewhat technical topics lately and thought you might enjoy a break. There is, however, a tie to quilting if you just read on.

This time a year my vegetable garden is in its fledgling stage. I am harvesting the winter onions and some salad greens and radishes, but the tomato and pepper plants are still spindly. The herb, corn, beans, cucumber, beets, and squash seeds have just sprouted and mostly I’m still seeing a lot of dirt.

But it is the potatoes that make the garden look legitimate.  I plant the seed potatoes in mid March and by now they are full bushes at least 18″ high. Every time I walk in I think “Wow! It looks like a garden! If you have never planted potatoes you should give it a go next year. Many years ago when someone suggested to me that I should plant potatoes, I wondered why would I do that. A potato is a potato, something you can just get at the store. How wrong I was!

Not only is it one of the first vegetables to harvest, but home grown potatoes are delicious. I plant the various varieties in the order in which I harvest them. I have experimented with lots of different kinds and now have my favorites. I start with early red Caribe potatoes, which I will start harvesting in a couple of weeks, as soon as the flowers start dropping. Then along come my favorite, Yukon Gold, and finally the storing potatoes. This year I have Kennebec.

From the first little new potatoes steamed and then tossed in chopped parsley and garlic infused olive oil, to the July 4th potato salad, roasted potatoes, baked potatoes and so much more, I love the potatoes and know that they are organically grown. Below is one of my favorite recipes and I think this is best with Yukon Golds.

So how does all this relate to quilting?

I’ve been eyeing the potato leaves as a possible fabric design.

PS. Did you know that many leaves have golden ratio proportions? If the narrow opening of the Golden Gauge Calipers is placed on the widest part of the potato leaf, the wider opening of the calipers is the height of the leaf.

Smashed Potatoes Recipe

One potato per serving (Yukon Gold are the best for this recipe)

olive oil, salt and pepper

1. Wash the potatoes and wrap each in aluminum foil.

2. Bake at 350 for one hour

3. Remove the foil and place the potatoes on a cookie sheet that has been rubbed with olive oil. Leave plenty of space between potatoes.

4. Rub the bottom of a small skillet (I use a cast iron skillet for the weight) with olive oil and then place it on top of a potato and press down until it squashes to a shape of a thick hamburger patty.

5. Brush the top of each potato with a little olive oil and sprinkle with salt and pepper.

6. Bake in a 500 degree oven for about 15 minutes then turn each potato and bake another 15 minutes or so until the potatoes are brown and crispy.

These have the taste of french fries without all the calories.

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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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## 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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## 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.