Learn · Design

Bringing order to the chaotic beauty of nature. 🌿

The golden ratio, the Fibonacci sequence, and the swirl in the Curl Jar logo.

φ ≈ 1.618 The golden ratio
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From Fibonacci squares, to the golden spiral, to our logo

Quick answer

The golden ratio is a proportion of approximately 1.618, a design principle and mathematical marvel that appears in the spirals of shells, branching trees, galaxies and possibly even curls. The swirl in the Curl Jar logo is inspired by it.

Lesson 01

It starts with a simple sequence

Start with 1 and 1. Add the last two numbers together to get the next one. Keep going and you have the Fibonacci sequence.

1
1
21+1
31+2
52+3
83+5
135+8
218+13
3413+21

Lesson 02

Divide, and you find 1.618

Divide each Fibonacci number by the one before it. The answer swings above and below, getting closer every time, to one number: the golden ratio, φ ≈ 1.618.

3 ÷ 21.500
5 ÷ 31.667
8 ÷ 51.600
13 ÷ 81.625
21 ÷ 131.615
34 ÷ 211.619

The golden ratio

1.618

Balance and aesthetic perfection, expressed as a number.

Lesson 03

An idea as old as design

The ratio was mentioned by early philosophers, artists and ancient architects as a way to bring order to the chaotic beauty of nature. With a value of approximately 1.618, it embodies balance and aesthetic perfection, and it's still used by designers today.

Lesson 04

Where you'll find it

🐚

Shells

The spirals of shells are some of the most famous examples people point to.

🌿

Branching trees

Branches, leaves and seed heads often grow in Fibonacci-like patterns.

🌌

Galaxies

Spiral galaxies sweep outward in shapes that echo the golden spiral.

➰

Possibly, curls

The same spiralling logic you see in nature may even show up in a curl.

The Curl Jar logo, with a swirl inspired by the golden ratio

The Curl Jar connection

The swirl in our logo

The swirl in the Curl Jar logo is inspired by this very concept. Factoring in nature's intrinsic beauty, we create products that work in harmony with the dynamic structure of curly hair.

Nature's order, in a jar. Made to work with your curls, not against them.

Good to know

Golden ratio FAQs

What is the golden ratio?

The golden ratio, often written as the Greek letter φ (phi), is a proportion of roughly 1.618. Two quantities are in the golden ratio when the larger one divided by the smaller equals their sum divided by the larger.

What is the Fibonacci sequence?

A sequence where each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on.

How are the Fibonacci sequence and the golden ratio connected?

Divide any Fibonacci number by the one before it and the answer gets closer and closer to 1.618, the golden ratio. Drawing quarter-circles through Fibonacci-sized squares creates the golden spiral.

Is the Curl Jar logo based on the golden ratio?

Yes. The swirl in the Curl Jar logo is inspired by the golden ratio and the spiral it creates.

Simple curl care, by design.

See what goes into the jar.

Shop Curl Activator Explore the ingredients