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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. 2. calipers open and closed 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.

3. calipers on oval
Oval A

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. calipers on compass 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.

two blocks side by side
Duck & Ducklings and Whirling Five Patch

The Whirling Five Patch with calipersUnknowingly, 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.

45 thoughts on “The Magical Golden Ratio

  1. Thanks Jinny. Found this facinating when you explained this in class last week (4/23). I have passed this info on to my fellow guild members.

  2. Good grief!!

  3. Thank you for acknowledging the fact that we quilters are not dummies…and we enjoy the entire dynamic of our craft. Although drafting our own designs is not always the norm…it is certainly a challenge that we can all attempt and feel so proud of! This is great information, and gets my mind and juices moving/flowing. 🙂 Keep treating us as if we are the smart and interested people that we really are!

  4. Never thought of this before but it makes perfect sense! I agree with you Jinny. I like the 5 x5 patch also. Very interesting. Thank you!

  5. Love learning about this. Your right about which looks better& I really never knew why.

  6. Thank you, Jinny
    You were my reason for starting quilting in the late 70’s. I love your fabrics and designs for quilts. This article will help me remember the golden ratio. Loved seeing your home and gardens on tv some years ago. Much success and happiness to you in the future.
    Sincerely, Joyce

  7. Jinny, you explain this so well. Thanks so much. I will await your blog.

  8. A fascinating lesson. Thank you for sharing.

  9. Thanks for this information. I found it fascinating.

  10. wow how brilliant is this,you are so clever. I remember doing this in school cheers Trish

  11. This is so facinating. How does the 1.618 relate to the Fibonicci numbers? They also repeat in math and nature. Also, garment proportions are discussed in fashion design and the suggested proportions are 1:1 or 1:2 or 2/5:3/5 or 1/3:2/3. The .618 is close to the 2/3 or the 3/5.

  12. This reminds me of the first time we visited the Taj Mahal in India. I could see the tiny model from the plane and expected to see it from the taxi as we approached, but no. We wound through the tiny streets and finally reached the gated entrance, but not a sight of the beautiful tomb. As we got down from the taxi and entered the main gate, it suddenly loomed in front of us as if it had risen from the earth itself. That grand presentation had to be a mathematical calculation. NOW I know why your quilts are so beautiful; not just the color combinations, but the symmetry too.

  13. How does this relate to fibanatchi numbers? (Prime) (leaves on branch?) (# of fronds…)

    1. We will have more on this in future blogs.

  14. As a retired math teacher of over 45 years I love that the Golden Ratio has made its way into quilting.

  15. Aha! so says the newbie. I auditioned a border around a block that cut the middle of the secondary pattern using a strip in the stash, thinking I was just looking for the right color and it didn’t appeal. I bet the reason I didn’t like it was the ratio was off and I didn’t even see the colors. Thx

  16. Fascinating! I now understand the Golden Triangle properly instead of it being rather fuzzy in my mind!
    Thank you!!

  17. I’m a visual learner by nature, and you have broken this lesson down into something I (we) can easily relate to and understand. Look forward to looking at borders and how to determine a pleasing size.
    Thank you for sharing….

  18. Printed this and put copy in mym’Stitchin’ Niotebook. What a keeper!

  19. This was wonderful!!! Thank you for taking the time to share this.
    How is the Golden Mean related to the Fibonacci series?
    How is the Golden Mean related to the Rule of Thirds?

    1. We will have more on this in future blogs.

      1. I’m really looking forward to that. I love learning this kind of stuff!


  20. I remember you teaching us about this in a class many years ago. You told of how you had to lecture at a math conference, and you were a little unsure how you would relate quilting to math.
    I remember being absolutely stunned when you told us this, and gave us the formula, (I still have the paper, and show it to anyone who will sit still long enough to digest it.) I told my husband about it immediately on the way home. (He was an engineer, in the nuclear power field) We went home and tested it out all over the place, and had so much fun doing it. Changed a few things in my house!
    You are and have been since the 70’s my favorite designer, my absolutely favorite quilter, (especially love all your geometric quilts, summer lilly, crayon box, moon glow, and the latest facets). Love your new Batik Malam collection, and hope you keep it like your palette, and add more to it. You are also the best teacher I have ever had. I hand quilt all of my quilts now, and seem to get a lot more quilting done because of being able to take it anywhere.
    Thank you so much, Jinny, for all you have done for me, and the quilting world. Mary

    1. Thanks so much for those very kind words, Mary.

  21. Dear Jinny,

    What a beautiful instrument. When I am in the States beginning of Oktober 2014, I hope to buy one at your shop (perhaps more for my frineds also).

    Thanks for your information. Dearest greetings.

    Trijntje Yntema

  22. Jinny,

    Is the golden caliper for sale and if so at what price? I really look forward to your e-mails and newsletters I have learned so much from you. I hope you will be attending the Houston quilt show this year. I hope to see you there.

  23. Thank you so much for pointing this out to me. Truthfully, I don’t think of proportions to this extent. I guess this shows I’m not a pro. It is a real eye opener for me and am looking forward to the future article regarding borders. Very enlightening. Happy Spring!

  24. This is a great yet simpler way to achieve the 1/3 to 2/3 ratio we learned in photography/art classes. Some people can ‘see’ it better than others, but the math involved to achieve it is sometimes tiring. We know that 9 patch is so popular because of this rule and gives quilters a great jumpstart to achieving quick success. This caliper tool is genious and should be in every artist’s toolbox to help define their designs more balanced. Love this article.

  25. Jinny, Thank you for explaining the golden rule. It truely makes sense and I look forward to using this information in future quilts.

  26. Thank you Jinny, for the fascinating detail in your explanation.
    Such a valuable lesson in design. I’ve often wondered why I like ‘what I like’ in quilt patterns and therefore want to develop knowledge/confidence in my choices in colour, balance, value, harmony, proportion, texture etc…
    I’m looking forward to learning more from you as I want to design and make a quilt for my adult son 🙂

  27. This is great!! more info I never before.

  28. Being “mathematically challenged,” I was awed and amazed by your knowledge and inventiveness. And all this on top of your incredible artistic creativeness. Am passing this on………. Thank you, Jinny

  29. OMG FAN_____TAS_____TIC information. LOVE your site. It is like going to college!!!!!!!

  30. WONDERFUL !! Now that John is no longer with me, I can do a lot of this kind o f stuff without his engineering help. THANKS for this info. What other goodies do you have for us ? This 82 yr old needs all the help I can get. You are one special terrific person. I am so happy that I came to know you so many, many years ago.

  31. I applaud your knowledge of this topic and your clear explanation and pictures of the golden ratio!

  32. My mind has been blown!!! Just moved this tool to the top of my must have list!! My biggest reason for not creating my own designs is a total lack of understanding of proportion!! I know there are pleasing proportions but never knew there was a way to achieve them. THANK YOU!!!

  33. I have been searching for the proportions for the Golden rule, and came across your calipers which I have just ordered . I can’ t wait for them to arrive. Fantastic. I do like to take a scientific approach and research for a project. Thanks Jinny.

  34. Thanks Jinny for sharing.
    In our development we have many cards players and I have been asked to join their groups. When I say no thanks, they always say you know it is good for the brain.
    I always respond with cards aren’t my thing, however I quilt, which is challenging enough.

  35. Thank you Jinny. I never understood the math.

  36. Hi Jinny,
    I have two Golden Calipers – one is a small and the other, a medium/large. I always design my own quilt layouts and I use them religiously. They help me ensure my blocks, sashes and borders compliment each other so when the quilts are assembled, they’re always visually pleasing.
    My Calipers are staple (must have) tools in my quilting studio and I wholeheartedly recommend to other fellow quilters, they add one to theirs.

  37. Jinny,
    I am working on a king sized quilt and need to put borders on it to make it the right size. To get a good balance should I first decide what the exact measurement I need, then use this golden rule to decide how to divide it? Also how large can the calipers get. Would I be able to use them to break up a large border in proper proportions? I love your fabrics and beautiful designs that you do.

    1. Thank you for your question, I believe our post this week will help answer your question, can’t wait to see what you come up with!

  38. What seems so simply still causes me to be unsure of my findings…I want to know how wide to make my inner border in proper proportion to my wider outer border.

    1. Wendy–here’s a link to an earlier blog by Jinny which might help:
      In it, Jinny explains the Golden Ratio:”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.”
      The calipers do the math for you. In the Wings quilt, the first border is 3/4″ or .75″. Doing the math, .75 x 1.618 = 1.21 or about an inch and a quarter for the wider border. If you are starting with the wider border and want to figure out the inner border, multiply it by .618.

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