Geometry in Quilting: The Fibonacci Sequence and Golden Ratio

Longtime quilters know that math is part of the process. Whether you're measuring quilt squares to get the perfect pattern or multiplying lengths and widths to find out how much fabric you might need, numbers are a part of the art. The more you know about numbers and math, the more unique and complex quilts you can make. Learn more about Fibonacci quilting below, including how to bring harmonious designs to your fabrics.

Who Was Fibonacci?

Fibonacci was a mathematician. He lived in Italy between around 1170 AD and 1240 AD under the name Leonardo Fibonacci or Leonardo Pisano. As a mathematician, he's known mainly for the Fibonacci Sequence, which is linked to something called the Golden Ratio.

What Is the Fibonacci Sequence?

A Fibonacci Sequence refers to a list of numbers that follows a specific mathematical pattern. The pattern is that every two numbers in the sequence add up to the next number. For example:

• The sequence 1, 1, 2, 3, 5, 8 is a Fibonacci Sequence. These are Fibonacci numbers because:

• 1+1 = 2

• 1+2 = 3

• 2+3 = 5

• 3+5 = 8

• The sequence 7, 7, 14, 21, 35, 56 is also a Fibonacci Sequence because:

• 7+7 = 14

• 7+14 = 21

• 14+21 = 35

• 21+35 = 56

What Is the Golden Ratio?

The Golden Ratio is another math concept, but it's one that's often used in art and design. The Golden Ratio is a number; it's around 1.618.

If you have two numbers (A and B) that work with the following math rulesets, then those two numbers form the Golden Ratio:

• A/B is equal to (A+B)/A and

• Those equations are roughly equal to 1.618

Using the Fibonacci Sequence, you can find groups of numbers that begin to create this ratio. Let's consider the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21.

• 2/1 is 2

• 3/2 is 1.5

• 5/3 is 1.667

• 8/5 is 1.6

• 13/8 is 1.625

• 21/13 is 1.615

You can see that the higher you go with Fibonacci numbers, the closer to the Golden Ratio you can get.

Fibonacci Quilting

So, what does all this have to do with quilting? First, understanding the Golden Ratio lets you create rectangles that have an especially pleasing visual appeal. Because the Golden Ratio is found in nature, including in flowers and plants, there's something about it that feels harmonious and enjoyable to many people who view it. Incorporating it into your quilts can make the patterns more visually pleasing to people.

To create a rectangle with Golden Ratio proportions, simply choose a number for the width, such as 1 inch. Then, multiple that by 1.618 to get the length. In this case, that would be 1.618 inches. You can see that exact fabrics, measurements, cuts and stitching would be required to ensure Golden Ratios throughout a quilt, so Fibonacci quilt patterns are not typically something to be tackled by beginners or those who don't like working down in the details.

But if you're detail-oriented and have the tools and patience to cut and sew exacting lines, Fibonacci and Golden Ratio quilt patterns can result in some of the most geometrically complex, visually stunning quilts you've ever made.

Fibonacci Quilt Patterns: The Fibonacci Spiral

You can create the Fibonacci Spiral by blocking various size squares together to form rectangles:

• Start with two square blocks that are the same size, such as 2-inch squares. Block them together.

• Along the top side, add a square that has a width equal to the rectangle created by the two smaller squares. In this case, it would be a 4-inch square.

• To the side, so that it's sewn along the side of the large square and one smaller square, add another block that's equal to the first measurement plus the second measurement (in this case, 6 inches).

• Working around in a spiral, add more blocks, always adding the widths of the last two squares together. So, in the example case, you would add a 10-inch square, and then a 16-inch square.

Each time you add a larger square, you create a larger rectangle. The more you add, the closer you get to the exact Golden Ratio with that larger square because you're using Fibonacci numbers to create your pattern.

If you were to start at the smallest square and begin drawing a curved line outward, cutting through two corners of every square and wrapping around and around, you would end up with a perfect Fibonacci spiral.

You might make one large Fibonacci rectangle with the Golden Ratio as a quilt. You could even stitch that spiral to add to the effect. Or, you can make numerous smaller ones and sew them together to create colorful spirals and other geometric patterns that add depth to your quilt.

Getting Started With Fibonacci Quilting

If you'd like to get started with a Fibonacci quilt pattern, decide whether you're going to cut your own squares or use pre-cut squares. Since you can create a Golden Ratio quilt pattern almost completely with various-sized squares, you might be able to start with pre-cuts to reduce some of the work. But the square sizes quickly grow, and you may need to measure, mark and cut your own at some point.

If you want to work in fairly large Fibonacci numbers, here's a tip: Don't look for fabric that adheres to those proportions. You can sew smaller pieces together — such as four squares or several triangles — to create a bigger piece. You can use fabric of the same color to make a large square or mix and match fabric colors and patterns to build even more complex visuals into your Fibonacci designs.